{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Matminer introduction - Predicting bulk modulus\n", "\n", "This notebook demonstrates some of the basic features of matminer.\n", "\n", "This notebook was last updated 06/07/21 for version 0.7.0 of matminer and verison 0.0.2 of figrecipes (which you can download by cloning the [figrecipes source repo](https://github.com/hackingmaterials/figrecipes)). \n", "\n", "\n", "**Note that in order to get the in-line plotting to work, you might need to start Jupyter notebook with a higher data rate, e.g., ``jupyter notebook --NotebookApp.iopub_data_rate_limit=1.0e10``. We recommend you do this before starting.**\n", "\n", "\n", "## Overview\n", "In this notebook, we will:\n", "1. Load and examine a dataset in a pandas dataframe\n", "2. Add descriptors to the dataframe using matminer\n", "3. Train, compare, and visualize several machine learning methods with scikit-learn and matminer FigRecipes.\n", "\n", "\n", "\n", "## 1. Load and process data set\n", "\n", "Matminer comes pre-loaded with several example data sets you can use. Below, we'll load a data set of computed elastic properties of materials which is sourced from the paper: \"Charting the complete elastic properties of inorganic crystalline compounds\", M. de Jong *et al.*, Sci. Data. 2 (2015) 150009." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Decoding objects from /Users/ardunn/alex/lbl/projects/common_env/dev_codes/matminer/matminer/datasets/elastic_tensor_2015.json.gz: 100%|##########| 4724/4724 [00:20<00:00, 5805.67it/s]" ] } ], "source": [ "from matminer.datasets.convenience_loaders import load_elastic_tensor\n", "df = load_elastic_tensor() # loads dataset in a pandas DataFrame object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1 A first look at the data set\n", "\n", "The data set comes as a pandas DataFrame, which is a kind of \"spreadsheet\" object in Python. DataFrames have several useful methods you can use to explore and clean the data, some of which we'll explore below." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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material_idformulansitesspace_groupvolumestructureelastic_anisotropyG_ReussG_VRHG_VoigtK_ReussK_VRHK_Voigtpoisson_ratiocompliance_tensorelastic_tensorelastic_tensor_original
0mp-10003Nb4CoSi12124194.419802[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068896.84453597.14160497.438674194.267623194.268884194.2701460.285701[[0.004385293093993, -0.0016070693558990002, -...[[311.33514638650246, 144.45092552856926, 126....[[311.33514638650246, 144.45092552856926, 126....
1mp-10010Al(CoSi)2516461.987320[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691093.93965096.25200698.564362173.647763175.449907177.2520500.268105[[0.0037715428949660003, -0.000844229828709, -...[[306.93357350984974, 88.02634955100905, 105.6...[[306.93357350984974, 88.02634955100905, 105.6...
2mp-10015SiOs222125.952539[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489120.962289130.112955139.263621295.077545295.077545295.0775450.307780[[0.0019959391925840004, -0.000433146670736000...[[569.5291276937579, 157.8517489654999, 157.85...[[569.5291276937579, 157.8517489654999, 157.85...
3mp-10021Ga46376.721433[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680512.20598915.10190117.99781249.02596349.13067049.2353770.360593[[0.021647143908635, -0.005207263618160001, -0...[[69.28798774976904, 34.7875015216915, 37.3877...[[70.13259066665267, 40.60474945058445, 37.387...
4mp-10025SiRu21262160.300999[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930100.110773101.947798103.784823255.055257256.768081258.4809040.324682[[0.00410214297725, -0.001272204332729, -0.001...[[349.3767766177825, 186.67131003104407, 176.4...[[407.4791016459293, 176.4759188081947, 213.83...
\n", "
" ], "text/plain": [ " material_id formula nsites space_group volume \\\n", "0 mp-10003 Nb4CoSi 12 124 194.419802 \n", "1 mp-10010 Al(CoSi)2 5 164 61.987320 \n", "2 mp-10015 SiOs 2 221 25.952539 \n", "3 mp-10021 Ga 4 63 76.721433 \n", "4 mp-10025 SiRu2 12 62 160.300999 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_Reuss G_VRH G_Voigt K_Reuss K_VRH K_Voigt \\\n", "0 96.844535 97.141604 97.438674 194.267623 194.268884 194.270146 \n", "1 93.939650 96.252006 98.564362 173.647763 175.449907 177.252050 \n", "2 120.962289 130.112955 139.263621 295.077545 295.077545 295.077545 \n", "3 12.205989 15.101901 17.997812 49.025963 49.130670 49.235377 \n", "4 100.110773 101.947798 103.784823 255.055257 256.768081 258.480904 \n", "\n", " poisson_ratio compliance_tensor \\\n", "0 0.285701 [[0.004385293093993, -0.0016070693558990002, -... \n", "1 0.268105 [[0.0037715428949660003, -0.000844229828709, -... \n", "2 0.307780 [[0.0019959391925840004, -0.000433146670736000... \n", "3 0.360593 [[0.021647143908635, -0.005207263618160001, -0... \n", "4 0.324682 [[0.00410214297725, -0.001272204332729, -0.001... \n", "\n", " elastic_tensor \\\n", "0 [[311.33514638650246, 144.45092552856926, 126.... \n", "1 [[306.93357350984974, 88.02634955100905, 105.6... \n", "2 [[569.5291276937579, 157.8517489654999, 157.85... \n", "3 [[69.28798774976904, 34.7875015216915, 37.3877... \n", "4 [[349.3767766177825, 186.67131003104407, 176.4... \n", "\n", " elastic_tensor_original \n", "0 [[311.33514638650246, 144.45092552856926, 126.... \n", "1 [[306.93357350984974, 88.02634955100905, 105.6... \n", "2 [[569.5291276937579, 157.8517489654999, 157.85... \n", "3 [[70.13259066665267, 40.60474945058445, 37.387... \n", "4 [[407.4791016459293, 176.4759188081947, 213.83... " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Removing unneeded columns from the data set\n", "\n", "The data set above has many columns - we won't need all this data for our modeling. We'll mainly be trying to predict ``K_VRH`` and ``G_VRH`` (the Voight-Reuss-Hill average of the bulk and shear modulus, respectively) and the ``elastic_anisotropy``. We can drop most of the other output data. We also don't need various metadata such as the ``cif`` string of the structure since the crystal structure is already embedded in the ``structure`` column." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Index(['material_id', 'formula', 'nsites', 'space_group', 'volume',\n", " 'structure', 'elastic_anisotropy', 'G_Reuss', 'G_VRH', 'G_Voigt',\n", " 'K_Reuss', 'K_VRH', 'K_Voigt', 'poisson_ratio', 'compliance_tensor',\n", " 'elastic_tensor', 'elastic_tensor_original'],\n", " dtype='object')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.columns" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "unwanted_columns = [\"volume\", \"nsites\", \"compliance_tensor\", \"elastic_tensor\", \n", " \"elastic_tensor_original\", \"K_Voigt\", \"G_Voigt\", \"K_Reuss\", \"G_Reuss\"]\n", "df = df.drop(unwanted_columns, axis=1)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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material_idformulaspace_groupstructureelastic_anisotropyG_VRHK_VRHpoisson_ratio
0mp-10003Nb4CoSi124[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068897.141604194.2688840.285701
1mp-10010Al(CoSi)2164[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691096.252006175.4499070.268105
2mp-10015SiOs221[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489130.112955295.0775450.307780
3mp-10021Ga63[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680515.10190149.1306700.360593
4mp-10025SiRu262[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930101.947798256.7680810.324682
\n", "
" ], "text/plain": [ " material_id formula space_group \\\n", "0 mp-10003 Nb4CoSi 124 \n", "1 mp-10010 Al(CoSi)2 164 \n", "2 mp-10015 SiOs 221 \n", "3 mp-10021 Ga 63 \n", "4 mp-10025 SiRu2 62 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_VRH K_VRH poisson_ratio \n", "0 97.141604 194.268884 0.285701 \n", "1 96.252006 175.449907 0.268105 \n", "2 130.112955 295.077545 0.307780 \n", "3 15.101901 49.130670 0.360593 \n", "4 101.947798 256.768081 0.324682 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3 Getting a feel for the data using descriptive statistics\n", "\n", "A pandas DataFrame includes a function called ``describe()`` that helps determine statistics for the various numerical / categorical columns in the data." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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space_groupelastic_anisotropyG_VRHK_VRHpoisson_ratio
count1181.0000001181.0000001181.0000001181.0000001181.000000
mean163.4038952.14501367.543145136.2596610.287401
std65.04073319.14009744.57940872.8869780.062177
min4.0000000.0000052.7221756.4761350.042582
25%124.0000000.14503034.11795976.4353500.249159
50%193.0000000.35528759.735163130.3827660.290198
75%221.0000000.92311791.332142189.5741940.328808
max229.000000397.297866522.921225435.6614870.467523
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" ], "text/plain": [ " space_group elastic_anisotropy G_VRH K_VRH \\\n", "count 1181.000000 1181.000000 1181.000000 1181.000000 \n", "mean 163.403895 2.145013 67.543145 136.259661 \n", "std 65.040733 19.140097 44.579408 72.886978 \n", "min 4.000000 0.000005 2.722175 6.476135 \n", "25% 124.000000 0.145030 34.117959 76.435350 \n", "50% 193.000000 0.355287 59.735163 130.382766 \n", "75% 221.000000 0.923117 91.332142 189.574194 \n", "max 229.000000 397.297866 522.921225 435.661487 \n", "\n", " poisson_ratio \n", "count 1181.000000 \n", "mean 0.287401 \n", "std 0.062177 \n", "min 0.042582 \n", "25% 0.249159 \n", "50% 0.290198 \n", "75% 0.328808 \n", "max 0.467523 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes, the ``describe()`` function will reveal outliers that indicate mistakes in the data. For example, negative hence unphysical minimum bulk/shear moduli or maximum bulk/shear moduli that are too high. In this case, the data looks ok at first glance; meaing that there are no clear problems with the ranges of the various properties. Therefore, and we won't filter out any data.\n", "\n", "Note that the ``describe()`` function only describes numerical columns by default." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Add descriptors to the data (\"featurization\")\n", "\n", "We are seeking to find relationships between the inputs (composition and crystal structure of a material) and outputs (elastic properties such as ``K_VRH``, ``G_VRH``, and ``elastic_anisotropy``). To find such relations, we need to \"featurize\" the input data such that they are numbers that meaningfully represent the underlying physical quantity. For example, one \"feature\" or \"descriptor\" of the composition of a material such as ``Nb4CoSi`` would be the standard deviation of the Pauling electronegativity of the elements in the compound (weighted by stoichiometry). Compositions with high values of this quantity would be more ionic and quantities with lower values would tend towards covalent or ionic. A descriptor of the crystal structure might be the average coordination number of sites; higher coordination numbers indicate more bonds and therefore might indicate stiffer materials. With matminer, we can start generating hundreds of possible descriptors using the descriptor library that is available. Data mining techniques can help narrow down which descriptors are the most relevant to the target problem using the available output data as a guide." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Add composition-based features\n", "\n", "A major class of featurizers available in matminer uses the chemical composition to featurize the input data. Let's add some composition based features to our DataFrame.\n", "\n", "The first step is to have a column representing the chemical composition as a pymatgen Composition object. One way to do this is to use the conversions Featurizers in matminer to turn a String composition (our ``formula`` column from before) into a pymatgen Composition." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Reading file /Users/ardunn/alex/lbl/projects/common_env/dev_codes/matminer/matminer/datasets/elastic_tensor_2015.json.gz: 4724it [01:29, 52.69it/s] \n", "Decoding objects from /Users/ardunn/alex/lbl/projects/common_env/dev_codes/matminer/matminer/datasets/elastic_tensor_2015.json.gz: 100%|##########| 4724/4724 [01:29<00:00, 52.69it/s] \n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6d44b1c49cdd4d59b52628768aaf9c94", "version_major": 2, "version_minor": 0 }, "text/plain": [ "StrToComposition: 0%| | 0/1181 [00:00\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
material_idformulaspace_groupstructureelastic_anisotropyG_VRHK_VRHpoisson_ratiocomposition
0mp-10003Nb4CoSi124[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068897.141604194.2688840.285701(Nb, Co, Si)
1mp-10010Al(CoSi)2164[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691096.252006175.4499070.268105(Al, Co, Si)
2mp-10015SiOs221[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489130.112955295.0775450.307780(Si, Os)
3mp-10021Ga63[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680515.10190149.1306700.360593(Ga)
4mp-10025SiRu262[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930101.947798256.7680810.324682(Si, Ru)
\n", "" ], "text/plain": [ " material_id formula space_group \\\n", "0 mp-10003 Nb4CoSi 124 \n", "1 mp-10010 Al(CoSi)2 164 \n", "2 mp-10015 SiOs 221 \n", "3 mp-10021 Ga 63 \n", "4 mp-10025 SiRu2 62 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_VRH K_VRH poisson_ratio composition \n", "0 97.141604 194.268884 0.285701 (Nb, Co, Si) \n", "1 96.252006 175.449907 0.268105 (Al, Co, Si) \n", "2 130.112955 295.077545 0.307780 (Si, Os) \n", "3 15.101901 49.130670 0.360593 (Ga) \n", "4 101.947798 256.768081 0.324682 (Si, Ru) " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matminer.featurizers.conversions import StrToComposition\n", "df = StrToComposition().featurize_dataframe(df, \"formula\")\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, we now have a new Composition column above. The visualization in the DataFrame is not so clear, but the column embeds both the elements *and* the amounts of each element in the composition (not shown).\n", "\n", "Next, we'll use one of the featurizers in matminer to add a suite of descriptors to the DataFrame." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fe7870d7d1ed40d195e6c9c65a3c2a06", "version_major": 2, "version_minor": 0 }, "text/plain": [ "ElementProperty: 0%| | 0/1181 [00:00\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
material_idformulaspace_groupstructureelastic_anisotropyG_VRHK_VRHpoisson_ratiocompositionMagpieData minimum Number...MagpieData range GSmagmomMagpieData mean GSmagmomMagpieData avg_dev GSmagmomMagpieData mode GSmagmomMagpieData minimum SpaceGroupNumberMagpieData maximum SpaceGroupNumberMagpieData range SpaceGroupNumberMagpieData mean SpaceGroupNumberMagpieData avg_dev SpaceGroupNumberMagpieData mode SpaceGroupNumber
0mp-10003Nb4CoSi124[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068897.141604194.2688840.285701(Nb, Co, Si)14.0...1.5484710.2580790.4301310.0194.0229.035.0222.8333339.611111229.0
1mp-10010Al(CoSi)2164[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691096.252006175.4499070.268105(Al, Co, Si)13.0...1.5484710.6193880.7432660.0194.0227.033.0213.40000015.520000194.0
2mp-10015SiOs221[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489130.112955295.0775450.307780(Si, Os)14.0...0.0000000.0000000.0000000.0194.0227.033.0210.50000016.500000194.0
3mp-10021Ga63[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680515.10190149.1306700.360593(Ga)31.0...0.0000000.0000000.0000000.064.064.00.064.0000000.00000064.0
4mp-10025SiRu262[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930101.947798256.7680810.324682(Si, Ru)14.0...0.0000000.0000000.0000000.0194.0227.033.0205.00000014.666667194.0
\n", "

5 rows × 141 columns

\n", "" ], "text/plain": [ " material_id formula space_group \\\n", "0 mp-10003 Nb4CoSi 124 \n", "1 mp-10010 Al(CoSi)2 164 \n", "2 mp-10015 SiOs 221 \n", "3 mp-10021 Ga 63 \n", "4 mp-10025 SiRu2 62 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_VRH K_VRH poisson_ratio composition \\\n", "0 97.141604 194.268884 0.285701 (Nb, Co, Si) \n", "1 96.252006 175.449907 0.268105 (Al, Co, Si) \n", "2 130.112955 295.077545 0.307780 (Si, Os) \n", "3 15.101901 49.130670 0.360593 (Ga) \n", "4 101.947798 256.768081 0.324682 (Si, Ru) \n", "\n", " MagpieData minimum Number ... MagpieData range GSmagmom \\\n", "0 14.0 ... 1.548471 \n", "1 13.0 ... 1.548471 \n", "2 14.0 ... 0.000000 \n", "3 31.0 ... 0.000000 \n", "4 14.0 ... 0.000000 \n", "\n", " MagpieData mean GSmagmom MagpieData avg_dev GSmagmom \\\n", "0 0.258079 0.430131 \n", "1 0.619388 0.743266 \n", "2 0.000000 0.000000 \n", "3 0.000000 0.000000 \n", "4 0.000000 0.000000 \n", "\n", " MagpieData mode GSmagmom MagpieData minimum SpaceGroupNumber \\\n", "0 0.0 194.0 \n", "1 0.0 194.0 \n", "2 0.0 194.0 \n", "3 0.0 64.0 \n", "4 0.0 194.0 \n", "\n", " MagpieData maximum SpaceGroupNumber MagpieData range SpaceGroupNumber \\\n", "0 229.0 35.0 \n", "1 227.0 33.0 \n", "2 227.0 33.0 \n", "3 64.0 0.0 \n", "4 227.0 33.0 \n", "\n", " MagpieData mean SpaceGroupNumber MagpieData avg_dev SpaceGroupNumber \\\n", "0 222.833333 9.611111 \n", "1 213.400000 15.520000 \n", "2 210.500000 16.500000 \n", "3 64.000000 0.000000 \n", "4 205.000000 14.666667 \n", "\n", " MagpieData mode SpaceGroupNumber \n", "0 229.0 \n", "1 194.0 \n", "2 194.0 \n", "3 64.0 \n", "4 194.0 \n", "\n", "[5 rows x 141 columns]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matminer.featurizers.composition import ElementProperty\n", "\n", "ep_feat = ElementProperty.from_preset(preset_name=\"magpie\")\n", "df = ep_feat.featurize_dataframe(df, col_id=\"composition\") # input the \"composition\" column to the featurizer\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, we now have many more columns in the DataFrame (a total of 141 columns - not all are shown). So we added *many* features to our data!\n", "\n", "As an aside, note that each featurizer also has a ``citations()`` function that tells you where to find out more about the Featurizer." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['@article{ward_agrawal_choudary_wolverton_2016, title={A general-purpose machine learning framework for predicting properties of inorganic materials}, volume={2}, DOI={10.1038/npjcompumats.2017.28}, number={1}, journal={npj Computational Materials}, author={Ward, Logan and Agrawal, Ankit and Choudhary, Alok and Wolverton, Christopher}, year={2016}}']" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ep_feat.citations()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Add more composition-based features\n", "\n", "There are many more Composition based featurizers apart from ``ElementProperty`` that are available in the ``matminer.featurizers.composition``. Let's try the ``ElectronegativityDiff`` featurizer which requires knowing the oxidation state of the various elements in the Composition. This information is not there currently, but one can use the ``conversions`` package to try to guess oxidation states and then apply the ``ElectronegativityDiff`` featurizer to this column." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f6cdfd755c5b4b6393dd62318d0502ec", "version_major": 2, "version_minor": 0 }, "text/plain": [ "CompositionToOxidComposition: 0%| | 0/1181 [00:00\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
material_idformulaspace_groupstructureelastic_anisotropyG_VRHK_VRHpoisson_ratiocompositionMagpieData minimum Number...MagpieData maximum SpaceGroupNumberMagpieData range SpaceGroupNumberMagpieData mean SpaceGroupNumberMagpieData avg_dev SpaceGroupNumberMagpieData mode SpaceGroupNumbercomposition_oxidminimum oxidation statemaximum oxidation staterange oxidation statestd_dev oxidation state
0mp-10003Nb4CoSi124[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068897.141604194.2688840.285701(Nb, Co, Si)14.0...229.035.0222.8333339.611111229.0(Nb0+, Co0+, Si0+)0000.000000
1mp-10010Al(CoSi)2164[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691096.252006175.4499070.268105(Al, Co, Si)13.0...227.033.0213.40000015.520000194.0(Al3+, Co2+, Co3+, Si4-)-4373.872983
2mp-10015SiOs221[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489130.112955295.0775450.307780(Si, Os)14.0...227.033.0210.50000016.500000194.0(Si4-, Os4+)-4485.656854
3mp-10021Ga63[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680515.10190149.1306700.360593(Ga)31.0...64.00.064.0000000.00000064.0(Ga0+)0000.000000
4mp-10025SiRu262[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930101.947798256.7680810.324682(Si, Ru)14.0...227.033.0205.00000014.666667194.0(Si4-, Ru2+)-4264.242641
\n", "

5 rows × 146 columns

\n", "" ], "text/plain": [ " material_id formula space_group \\\n", "0 mp-10003 Nb4CoSi 124 \n", "1 mp-10010 Al(CoSi)2 164 \n", "2 mp-10015 SiOs 221 \n", "3 mp-10021 Ga 63 \n", "4 mp-10025 SiRu2 62 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_VRH K_VRH poisson_ratio composition \\\n", "0 97.141604 194.268884 0.285701 (Nb, Co, Si) \n", "1 96.252006 175.449907 0.268105 (Al, Co, Si) \n", "2 130.112955 295.077545 0.307780 (Si, Os) \n", "3 15.101901 49.130670 0.360593 (Ga) \n", "4 101.947798 256.768081 0.324682 (Si, Ru) \n", "\n", " MagpieData minimum Number ... MagpieData maximum SpaceGroupNumber \\\n", "0 14.0 ... 229.0 \n", "1 13.0 ... 227.0 \n", "2 14.0 ... 227.0 \n", "3 31.0 ... 64.0 \n", "4 14.0 ... 227.0 \n", "\n", " MagpieData range SpaceGroupNumber MagpieData mean SpaceGroupNumber \\\n", "0 35.0 222.833333 \n", "1 33.0 213.400000 \n", "2 33.0 210.500000 \n", "3 0.0 64.000000 \n", "4 33.0 205.000000 \n", "\n", " MagpieData avg_dev SpaceGroupNumber MagpieData mode SpaceGroupNumber \\\n", "0 9.611111 229.0 \n", "1 15.520000 194.0 \n", "2 16.500000 194.0 \n", "3 0.000000 64.0 \n", "4 14.666667 194.0 \n", "\n", " composition_oxid minimum oxidation state maximum oxidation state \\\n", "0 (Nb0+, Co0+, Si0+) 0 0 \n", "1 (Al3+, Co2+, Co3+, Si4-) -4 3 \n", "2 (Si4-, Os4+) -4 4 \n", "3 (Ga0+) 0 0 \n", "4 (Si4-, Ru2+) -4 2 \n", "\n", " range oxidation state std_dev oxidation state \n", "0 0 0.000000 \n", "1 7 3.872983 \n", "2 8 5.656854 \n", "3 0 0.000000 \n", "4 6 4.242641 \n", "\n", "[5 rows x 146 columns]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matminer.featurizers.conversions import CompositionToOxidComposition\n", "from matminer.featurizers.composition import OxidationStates\n", "\n", "df = CompositionToOxidComposition().featurize_dataframe(df, \"composition\")\n", "\n", "os_feat = OxidationStates()\n", "df = os_feat.featurize_dataframe(df, \"composition_oxid\")\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the end of our data frame has now has some oxidation state based features!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Add some structure based features\n", "\n", "Not all featurizers operate on compositions. Matminer can also analyze crystal structures and featurize those as well. Let's start by adding some simple density features." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c9ae86a85b41492f8d6a821ac003d987", "version_major": 2, "version_minor": 0 }, "text/plain": [ "DensityFeatures: 0%| | 0/1181 [00:00\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
material_idformulaspace_groupstructureelastic_anisotropyG_VRHK_VRHpoisson_ratiocompositionMagpieData minimum Number...MagpieData avg_dev SpaceGroupNumberMagpieData mode SpaceGroupNumbercomposition_oxidminimum oxidation statemaximum oxidation staterange oxidation statestd_dev oxidation statedensityvpapacking fraction
0mp-10003Nb4CoSi124[[0.94814328 2.07280467 2.5112 ] Nb, [5.273...0.03068897.141604194.2688840.285701(Nb, Co, Si)14.0...9.611111229.0(Nb0+, Co0+, Si0+)0000.0000007.83455616.2016540.688834
1mp-10010Al(CoSi)2164[[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278...0.26691096.252006175.4499070.268105(Al, Co, Si)13.0...15.520000194.0(Al3+, Co2+, Co3+, Si4-)-4373.8729835.38496812.3974660.644386
2mp-10015SiOs221[[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os]0.756489130.112955295.0775450.307780(Si, Os)14.0...16.500000194.0(Si4-, Os4+)-4485.65685413.96863512.9762650.569426
3mp-10021Ga63[[0. 1.09045794 0.84078375] Ga, [0. ...2.37680515.10190149.1306700.360593(Ga)31.0...0.00000064.0(Ga0+)0000.0000006.03626719.1803590.479802
4mp-10025SiRu262[[1.0094265 4.24771709 2.9955487 ] Si, [3.028...0.196930101.947798256.7680810.324682(Si, Ru)14.0...14.666667194.0(Si4-, Ru2+)-4264.2426419.53951413.3584180.598395
\n", "

5 rows × 149 columns

\n", "" ], "text/plain": [ " material_id formula space_group \\\n", "0 mp-10003 Nb4CoSi 124 \n", "1 mp-10010 Al(CoSi)2 164 \n", "2 mp-10015 SiOs 221 \n", "3 mp-10021 Ga 63 \n", "4 mp-10025 SiRu2 62 \n", "\n", " structure elastic_anisotropy \\\n", "0 [[0.94814328 2.07280467 2.5112 ] Nb, [5.273... 0.030688 \n", "1 [[0. 0. 0.] Al, [1.96639263 1.13529553 0.75278... 0.266910 \n", "2 [[1.480346 1.480346 1.480346] Si, [0. 0. 0.] Os] 0.756489 \n", "3 [[0. 1.09045794 0.84078375] Ga, [0. ... 2.376805 \n", "4 [[1.0094265 4.24771709 2.9955487 ] Si, [3.028... 0.196930 \n", "\n", " G_VRH K_VRH poisson_ratio composition \\\n", "0 97.141604 194.268884 0.285701 (Nb, Co, Si) \n", "1 96.252006 175.449907 0.268105 (Al, Co, Si) \n", "2 130.112955 295.077545 0.307780 (Si, Os) \n", "3 15.101901 49.130670 0.360593 (Ga) \n", "4 101.947798 256.768081 0.324682 (Si, Ru) \n", "\n", " MagpieData minimum Number ... MagpieData avg_dev SpaceGroupNumber \\\n", "0 14.0 ... 9.611111 \n", "1 13.0 ... 15.520000 \n", "2 14.0 ... 16.500000 \n", "3 31.0 ... 0.000000 \n", "4 14.0 ... 14.666667 \n", "\n", " MagpieData mode SpaceGroupNumber composition_oxid \\\n", "0 229.0 (Nb0+, Co0+, Si0+) \n", "1 194.0 (Al3+, Co2+, Co3+, Si4-) \n", "2 194.0 (Si4-, Os4+) \n", "3 64.0 (Ga0+) \n", "4 194.0 (Si4-, Ru2+) \n", "\n", " minimum oxidation state maximum oxidation state range oxidation state \\\n", "0 0 0 0 \n", "1 -4 3 7 \n", "2 -4 4 8 \n", "3 0 0 0 \n", "4 -4 2 6 \n", "\n", " std_dev oxidation state density vpa packing fraction \n", "0 0.000000 7.834556 16.201654 0.688834 \n", "1 3.872983 5.384968 12.397466 0.644386 \n", "2 5.656854 13.968635 12.976265 0.569426 \n", "3 0.000000 6.036267 19.180359 0.479802 \n", "4 4.242641 9.539514 13.358418 0.598395 \n", "\n", "[5 rows x 149 columns]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matminer.featurizers.structure import DensityFeatures\n", "\n", "df_feat = DensityFeatures()\n", "df = df_feat.featurize_dataframe(df, \"structure\") # input the structure column to the featurizer\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['density', 'vpa', 'packing fraction']" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_feat.feature_labels()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we see more features in the last few columns: ``density``, ``vpa``, and ``packing fraction``.\n", "\n", "There are many more structure based featurizers that are much more complex and detailed analysis of the crystal structure that are outside of the scope of this example. Let's move on to doing some machine learning predictions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Try some different machine learning models to relate input features to the bulk modulus\n", "\n", "We now have enough data to do some machine learning! We'll need to first determine what columns we consider input (independent variables) and what column we consider output (dependent variable).\n", "\n", "## 3.1 Define input data and output data\n", "\n", "For now, we'll use ``K_VRH`` (bulk modulus) as the output. You could retry this example with ``G_VRH``, ``elastic_anisotropy``, or ``poisson_ratio`` as the target output.\n", "\n", "For the inputs, we'll use all the features we generated. That is, everything except the output data and non-numerical columns like ``composition`` and ``structure``.\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There are 140 possible descriptors:\n", "\n", "['space_group' 'MagpieData minimum Number' 'MagpieData maximum Number'\n", " 'MagpieData range Number' 'MagpieData mean Number'\n", " 'MagpieData avg_dev Number' 'MagpieData mode Number'\n", " 'MagpieData minimum MendeleevNumber' 'MagpieData maximum MendeleevNumber'\n", " 'MagpieData range MendeleevNumber' 'MagpieData mean MendeleevNumber'\n", " 'MagpieData avg_dev MendeleevNumber' 'MagpieData mode MendeleevNumber'\n", " 'MagpieData minimum AtomicWeight' 'MagpieData maximum AtomicWeight'\n", " 'MagpieData range AtomicWeight' 'MagpieData mean AtomicWeight'\n", " 'MagpieData avg_dev AtomicWeight' 'MagpieData mode AtomicWeight'\n", " 'MagpieData minimum MeltingT' 'MagpieData maximum MeltingT'\n", " 'MagpieData range MeltingT' 'MagpieData mean MeltingT'\n", " 'MagpieData avg_dev MeltingT' 'MagpieData mode MeltingT'\n", " 'MagpieData minimum Column' 'MagpieData maximum Column'\n", " 'MagpieData range Column' 'MagpieData mean Column'\n", " 'MagpieData avg_dev Column' 'MagpieData mode Column'\n", " 'MagpieData minimum Row' 'MagpieData maximum Row' 'MagpieData range Row'\n", " 'MagpieData mean Row' 'MagpieData avg_dev Row' 'MagpieData mode Row'\n", " 'MagpieData minimum CovalentRadius' 'MagpieData maximum CovalentRadius'\n", " 'MagpieData range CovalentRadius' 'MagpieData mean CovalentRadius'\n", " 'MagpieData avg_dev CovalentRadius' 'MagpieData mode CovalentRadius'\n", " 'MagpieData minimum Electronegativity'\n", " 'MagpieData maximum Electronegativity'\n", " 'MagpieData range Electronegativity' 'MagpieData mean Electronegativity'\n", " 'MagpieData avg_dev Electronegativity'\n", " 'MagpieData mode Electronegativity' 'MagpieData minimum NsValence'\n", " 'MagpieData maximum NsValence' 'MagpieData range NsValence'\n", " 'MagpieData mean NsValence' 'MagpieData avg_dev NsValence'\n", " 'MagpieData mode NsValence' 'MagpieData minimum NpValence'\n", " 'MagpieData maximum NpValence' 'MagpieData range NpValence'\n", " 'MagpieData mean NpValence' 'MagpieData avg_dev NpValence'\n", " 'MagpieData mode NpValence' 'MagpieData minimum NdValence'\n", " 'MagpieData maximum NdValence' 'MagpieData range NdValence'\n", " 'MagpieData mean NdValence' 'MagpieData avg_dev NdValence'\n", " 'MagpieData mode NdValence' 'MagpieData minimum NfValence'\n", " 'MagpieData maximum NfValence' 'MagpieData range NfValence'\n", " 'MagpieData mean NfValence' 'MagpieData avg_dev NfValence'\n", " 'MagpieData mode NfValence' 'MagpieData minimum NValence'\n", " 'MagpieData maximum NValence' 'MagpieData range NValence'\n", " 'MagpieData mean NValence' 'MagpieData avg_dev NValence'\n", " 'MagpieData mode NValence' 'MagpieData minimum NsUnfilled'\n", " 'MagpieData maximum NsUnfilled' 'MagpieData range NsUnfilled'\n", " 'MagpieData mean NsUnfilled' 'MagpieData avg_dev NsUnfilled'\n", " 'MagpieData mode NsUnfilled' 'MagpieData minimum NpUnfilled'\n", " 'MagpieData maximum NpUnfilled' 'MagpieData range NpUnfilled'\n", " 'MagpieData mean NpUnfilled' 'MagpieData avg_dev NpUnfilled'\n", " 'MagpieData mode NpUnfilled' 'MagpieData minimum NdUnfilled'\n", " 'MagpieData maximum NdUnfilled' 'MagpieData range NdUnfilled'\n", " 'MagpieData mean NdUnfilled' 'MagpieData avg_dev NdUnfilled'\n", " 'MagpieData mode NdUnfilled' 'MagpieData minimum NfUnfilled'\n", " 'MagpieData maximum NfUnfilled' 'MagpieData range NfUnfilled'\n", " 'MagpieData mean NfUnfilled' 'MagpieData avg_dev NfUnfilled'\n", " 'MagpieData mode NfUnfilled' 'MagpieData minimum NUnfilled'\n", " 'MagpieData maximum NUnfilled' 'MagpieData range NUnfilled'\n", " 'MagpieData mean NUnfilled' 'MagpieData avg_dev NUnfilled'\n", " 'MagpieData mode NUnfilled' 'MagpieData minimum GSvolume_pa'\n", " 'MagpieData maximum GSvolume_pa' 'MagpieData range GSvolume_pa'\n", " 'MagpieData mean GSvolume_pa' 'MagpieData avg_dev GSvolume_pa'\n", " 'MagpieData mode GSvolume_pa' 'MagpieData minimum GSbandgap'\n", " 'MagpieData maximum GSbandgap' 'MagpieData range GSbandgap'\n", " 'MagpieData mean GSbandgap' 'MagpieData avg_dev GSbandgap'\n", " 'MagpieData mode GSbandgap' 'MagpieData minimum GSmagmom'\n", " 'MagpieData maximum GSmagmom' 'MagpieData range GSmagmom'\n", " 'MagpieData mean GSmagmom' 'MagpieData avg_dev GSmagmom'\n", " 'MagpieData mode GSmagmom' 'MagpieData minimum SpaceGroupNumber'\n", " 'MagpieData maximum SpaceGroupNumber' 'MagpieData range SpaceGroupNumber'\n", " 'MagpieData mean SpaceGroupNumber' 'MagpieData avg_dev SpaceGroupNumber'\n", " 'MagpieData mode SpaceGroupNumber' 'minimum oxidation state'\n", " 'maximum oxidation state' 'range oxidation state'\n", " 'std_dev oxidation state' 'density' 'vpa' 'packing fraction']\n" ] } ], "source": [ "y = df['K_VRH'].values\n", "excluded = [\"G_VRH\", \"K_VRH\", \"elastic_anisotropy\", \"formula\", \"material_id\", \n", " \"poisson_ratio\", \"structure\", \"composition\", \"composition_oxid\"]\n", "X = df.drop(excluded, axis=1)\n", "print(\"There are {} possible descriptors:\\n\\n{}\".format(X.shape[1], X.columns.values))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 Try a linear regression model using scikit-learn\n", "\n", "The scikit-learn library makes it easy to fit and cross-validate different types of regression models. Let's start with one of the simplest - a linear regression." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "training R2 = 0.927\n", "training RMSE = 19.625\n" ] } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import mean_squared_error\n", "import numpy as np\n", "\n", "lr = LinearRegression()\n", "\n", "lr.fit(X, y)\n", "\n", "# get fit statistics\n", "print('training R2 = ' + str(round(lr.score(X, y), 3)))\n", "print('training RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y, y_pred=lr.predict(X))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks reasonable since linear regression is a simple (high bias) model. But to really validate that we are not over-fitting, we need to check the cross-validation score rather than the fitting score." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cross-validation results:\n", "Folds: 10, mean R2: 0.902\n", "Folds: 10, mean RMSE: 22.467\n" ] } ], "source": [ "from sklearn.model_selection import KFold, cross_val_score\n", "\n", "# Use 10-fold cross validation (90% training, 10% test)\n", "crossvalidation = KFold(n_splits=10, shuffle=True, random_state=1)\n", "scores = cross_val_score(lr, X, y, scoring='neg_mean_squared_error', cv=crossvalidation, n_jobs=1)\n", "rmse_scores = [np.sqrt(abs(s)) for s in scores]\n", "r2_scores = cross_val_score(lr, X, y, scoring='r2', cv=crossvalidation, n_jobs=1)\n", "\n", "print('Cross-validation results:')\n", "print('Folds: %i, mean R2: %.3f' % (len(scores), np.mean(np.abs(r2_scores))))\n", "print('Folds: %i, mean RMSE: %.3f' % (len(scores), np.mean(np.abs(rmse_scores))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A root-mean-squared error of ~22 GPa is not bad! Let's see what this looks like on a plot.\n", "\n", "**Note that in order to get the code below to work, you might need to start Jupyter notebook with a higher data rate, e.g., ``jupyter notebook --NotebookApp.iopub_data_rate_limit=1.0e10``.**" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hidePrompt": true }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "hoverinfo": "x+y+text", "hoverlabel": { "font": { "family": "Courier", "size": 25 } }, "marker": { "colorscale": [ [ 0, "#440154" ], [ 0.1111111111111111, "#482878" ], [ 0.2222222222222222, "#3e4989" ], [ 0.3333333333333333, "#31688e" ], [ 0.4444444444444444, "#26828e" ], [ 0.5555555555555556, "#1f9e89" ], [ 0.6666666666666666, "#35b779" ], [ 0.7777777777777778, "#6ece58" ], [ 0.8888888888888888, "#b5de2b" ], [ 1, "#fde725" ] ], "line": { "color": "black", "width": 1 }, "showscale": false, "size": 10, "symbol": "circle" }, "mode": "markers", "showlegend": false, "text": [ "Nb4CoSi", "Al(CoSi)2", "SiOs", "Ga", "SiRu2", "AlCo3C", "CdSnSb2", "Ir", "SbIr", "MnSbIr", "Na", "Li", "Li2SbPd", "MgSbPd", "MgSbPt", "Co", "TaRh3", "Hf3(SiCu)4", "ZnFe3C", "HfRh3", "ScCo3C", "ZnCo3C", "BaF2", "Hf", "SbPt7", "MgCu2", "Ta2O5", "Sb", "HfSi", "Y(AlSi)2", "HfSiPt", "HfSiPd", "NbSn2", "NbSiPt", "NbSiRh", "Y2AlSi2", "Al3Ni2", "Ag", "CuSn", "Y3SnC", "SnSb", "LiAl", "Sc2AlSi2", "HfSi2", "ZnS", "VSi2", "ScRh3C", "Ti2C", "CaCd", "Si3Pt2", "Mg2SiCu3", "TiFeSb", "GeSe", "CaCd2", "VIr3", "TaC", "ScAlAu2", "Ca3Al7Cu2", "Ca(Al2Cu)4", "AlCrCo2", "AlFeCo2", "Al3Cu2", "HfAlCu2", "TiIr3", "LiAl3", "MnAlPd2", "MnAlPt", "Mn2AlV", "Al3Pd2", "AlPt", "Al3Pt2", "AlRe2", "Al2Ru", "Sc2Al3Ru", "As", "Y(Al2Cu)4", "BaO2", "Mn5Si3", "Ca3(SiIr)4", "VSi2", "CrSi2", "Y", "Mo3Ir", "Sc6FeSb2", "Y6FeSb2", "Sc2Al", "Al12W", "YAl", "YAl", "Y2Al", "YAl3", "LiAu3", "Mg2Au", "MnAu2", "ScAu", "TiAu", "YAu", "MnBe2", "Be2Nb3", "Be3Nb", "Be2Re", "BeRh", "ScBe5", "Ta2Be", "TiBe", "SiIr", "TiBe12", "Be2V", "Be2W", "CaHg", "CaHg2", "Ca3Hg2", "ScIr", "CaSn3", "Cd2Hg", "Tc", "TiCdHg2", "MgCd", "NbPd3", "CaAl9Co2", "TaCo3", "MgCuSn", "TiCu", "LiF", "YFe5", "Co3Mo", "Al2O3", "HfMn2", "TiB2", "HfOs", "HfPd3", "Hf2Pd", "HfPt", "HfPt3", "HfTc", "MgHg2", "Mg5Hg3", "Hg2Pt", "ScHg", "MoIr3", "Li3Pd", "Li2ZnSn", "YMg2", "MnZn3", "LiAl2Ir", "NbPt2", "NbRu3", "TiRh3", "NbAlRu2", "VPd2", "Sc2Pt", "ScRe2", "GaSb", "TiSiRu", "YRh5", "ScZn", "ScZn12", "YSn3", "TaTc", "TiTc", "VZn3", "Li2Ca", "ScCu", "TaSb2", "Sn", "MgRh", "MgSc", "Fe3Pt", "MnPt3", "LiPt", "TiAl2", "CaPd5", "VRh3", "HfSnPd", "Hg2Rh", "ZnSe", "CdPt", "CaSn2Ir", "CaSn2Pd", "CaSn2Rh", "LiSnAu", "CrIr3", "Cu3Pt", "NbSi2", "TiPt3", "VPt2", "ScCd", "Ca(ZnSi)2", "Te2O5", "Ba", "Be5Au", "CrSi2", "HgO", "Mo3Pt", "TiIr", "Ca5Sb3", "VRh", "TiCu3", "AlCuPt2", "AlNi3", "LiSbAu", "MnAu4", "HfBeSi", "Li2CdSn", "CrRh3", "ScIr3", "MoRh", "Pt", "CuPt7", "Ca2Cu", "TiAu4", "CdAu3", "Ti2Be17", "MgO", "HfAl2", "Mn2Nb", "Be12Pd", "MnAu", "MnAu", "TaMn2", "Mg2Rh", "YMgPd", "Sc(MnSn)6", "Ca3Au4", "Na", "NbPt3", "Cr3Ru", "CaAu", "MgPd2", "MgPd3", "SiMo3", "Zn2CuAu", "BeAu2", "YSi2", "Hf2Al", "AlCu3", "VOs", "Al2Cu", "AlCu3", "VIr", "VC", "PtO2", "Mo", "YCo2", "YAlPd", "SiPt2", "Ti2AlC", "Fe", "YSn2", "Mn2CoSi", "YMgAl", "Zr", "Cu3Sn", "Li12Si7", "Ti2Pd", "CoSb3", "YMgCu", "YMgCu4", "Ca", "YCuSn", "ScCuSn", "Mg2Pt", "CdSb", "YCd2", "Si3Mo5", "Y2C", "VFe", "SiPt3", "CaZn2", "NbIr3", "Al", "BaO", "LiSn", "Zn13Rh", "HfSb", "BePd2", "BePd3", "B6O", "HfSiRh", "Li", "ScZn2", "Sb2Pd", "ScSiPt2", "Sc2Si2Ru", "NbIr", "Mg2Si", "Ge", "Sn3Pd", "Zn3Ru", "AlV3", "Sr", "Sn4Au", "VRu", "AlAu", "Ga", "HfW2", "CdAu", "Ti3Sb", "Ga", "LiYSi", "TiCr2", "MnSi", "LiCd", "CaCd2", "Nb3Ir", "V", "Fe7W6", "Be12Mo", "BP", "Mg2SiPt", "SiRh", "AlNi", "Si", "AlAu4", "BaS", "Al3Pt5", "Al2Pt", "TiHg", "Mg", "ScSiCu", "Nb3Rh", "AlP", "Mo2C", "V3Sb", "Mg3Au", "CaSi", "TiCoSi", "Sb2Pt3", "Sc4C3", "V3Rh", "V3Co", "TiCr2", "Hf5Si3", "Hf3(SiCu2)2", "Li2CuSb", "TaRu", "NbAu2", "Cr3Ir", "Si2W", "CaSbAu", "CdSbAu", "CaZnSi", "Li2CdSb", "Sc3SnC", "CrSb", "Li3Hg", "Al12Re", "TiAlAu", "Al9Co2", "Fe3Pt", "YAl2Co", "ScAlCu2", "Si", "HfAlPd2", "Li3Al2", "Al3Ni5", "ZnPd", "Al3Os2", "Al2Pd", "Al3Pd5", "ScAlPd2", "AlPt2", "Al6Re", "Al6Ru", "V3Pd", "MnPt", "Al6Tc", "Al12Tc", "Y3Al2", "Be2Mo", "CdCu2", "Mg13Ir3", "HfRe2", "C", "Y2C3", "CdPd", "AlPt2", "AlCr2", "Hf3Rh5", "Sb2O5", "FeSi2", "CaZn2", "MnAl6", "Ti3Rh5", "CaAl4", "ZnAu3", "Y2Zn17", "SbPd", "Sc5Sn3", "SnAu", "Mg3Au", "ScRh", "Ti3Au", "Al5Rh2", "TaCo2", "Ti2Ni", "Ca3Cd2", "ScSnPt", "Ti3Al", "Cu2Sb", "Fe7C3", "Mg2Pd", "SiIr3", "NbAl3", "Nb2Al", "SnPd2", "Fe15Co", "Mg3Pt", "Fe2C", "AlPt3", "SnTe", "AlIr", "SiRu", "WC", "Te", "NiO", "YRh", "FeRh", "Nb3Os", "LiZn", "WO3", "Cr2O3", "TiMn2", "TiAl", "Cr5O12", "Li2O", "NbRh", "NbSb2", "YSiRh", "Fe11Si5", "MnCoSi", "Al21Pt8", "SnPt", "Ta5Si3", "Co2Si", "Hf2CuSb3", "YCuSb2", "Sn2Pt", "TiFe2Sn", "TiCuSn", "Pd", "SnIr", "ScSiCu", "MnSn2", "LiHg", "CoSn2", "AlFe3", "Si3Ru2", "HfMnSi", "HfBe5", "TiSiCu", "HfCo", "Be2Nb", "InAs", "Be2Cu", "W2C", "Ti6Sn5", "ScMn2", "HfSi2Cu", "MgCo3C", "TaSiRh", "Sn7Ir5", "Pb", "ScSiRh", "Nb3Sb", "CoSn", "VCo2Si", "SbRh", "SiPd3", "V2C", "Sn4Pt", "Co3SnC", "FeSb2", "HfCo2Sn", "FeSi2", "Pb", "TiCu", "Sn2Ir", "MnCo2Sn", "Ti5Sn3", "Mn3SnC", "Fe2W", "Fe3Sn", "FeCo", "Sb2Ru", "Cr3C2", "SnO", "SnPt3", "YZnSn", "Y2ReC2", "Si3Rh5", "Ti3SnC2", "CuAu3", "Hf3Si2", "YSiRu", "HfC", "Ti5Si3", "CaMnSi", "Hf5Sn3", "ScAl3", "Nb3Au2", "NbSiIr", "YMnSi", "TeO2", "HfIr3", "Sn4Pd", "LiSn4Ru", "CaPd", "TiCoSi", "TaSiIr", "ZnO", "V3Sn", "SbRh2", "Sb2O3", "VCoSi", "ZrRu", "MnSnPt", "YCoC", "TiCo2Sn", "VCo2Sn", "YSb", "Mg17Al12", "Co3W", "Sc2O3", "Li2Pt", "AlAs", "ZnTe", "FePd3", "Fe3SnC", "MnSiIr", "TiSb", "LiSn4Ir", "Fe3Si", "MnSnAu", "Sn7Ir3", "V3Pt", "ScCo", "YRh3C", "YTiSi", "Be2Fe", "HfSiMo", "Y(MnSn)6", "YSnPt", "ZnO", "Nb4FeSi", "HfCoSn", "Fe3Sn", "HfSiCu", "CrSb2", "YMn12", "MnSiRh", "Cu3Au", "FePt", "ScIr2", "ScFeSi", "NbSiPd", "Ca2Sn", "Mn5C2", "FeSn2", "Fe2Si", "AlFe3C", "NaCl", "RbBr", "SiRh", "KI", "RbI", "NaBr", "AgI", "Al3Ir", "Ni", "SbO2", "MoC", "CdO2", "Bi", "Nb2C", "KCl", "BeCu", "AgBr", "KBr", "Bi2O3", "NaI", "TiZn16", "RbCl", "HfCo2", "Ti3Pt", "Na2O2", "Mg2Sn", "YCd3", "Na2O", "Ti3Hg", "Hf5Al3", "HfMo2", "SnPd", "LiH", "CoSi2", "MnPd", "Sb3Rh", "YHg", "YPt3", "CaAl2", "CaMg2", "NbRh3", "YAl3", "TiFe2", "SrO", "NbSi2", "HfAl", "GaP", "AlCu", "CrPt3", "YZn", "Ca2Si", "ScCo2", "GaAs", "VTc", "BeO", "TeO3", "HfBe2", "Al3V", "Ti3Hg", "V3Si", "TiSi2", "TiRh", "YCo3", "AlMo3", "Si2Mo", "Ta5Sb4", "CaO", "HfAl3", "FeSb", "AlSb", "Ti3Cu4", "CoSb", "Mg3Sb2", "Al2Au", "TaIr3", "Y2O3", "AlFe", "Nb3Pt", "K2O2", "YPt2", "TaBe2", "ScPd3", "VPt", "Sb2Rh", "HgPd", "CdSe", "Sb2Os", "YCu2", "CaSi2", "VPt3", "Au2O3", "MnIr", "Sc2Co3Si", "Al8Mo3", "Nb5Sb4", "CaF2", "LiPd", "LiPd", "TiBe2", "Fe3Sn2", "Nb3Au", "Nb6C5", "YIr2", "BeCo", "ScPd", "Ta2Si", "LiIr", "Ti8C5", "Li7Si2", "Fe5C2", "HfRu", "YSiPd2", "AlPd2", "YCo5", "FePd", "AlCo", "SbPt", "VSb2", "GaN", "ZrO2", "TiOs", "Mn3ZnC", "Y2Si4Mo3", "Si5Pt6", "BaTiO3", "Cu", "YSi2Rh3", "Sb7Pd20", "Ca(AlZn)2", "Y(Al2Cr)4", "Al4Mo", "Ca2SiIr2", "Y3Al", "MgAl2Cu", "BeAu", "Hf2Au", "Li2SbAu", "Li2SnAu", "SnAu5", "CaSnPd", "Be2Cr", "Be17Nb2", "LiCaSn", "CaPt5", "CaZn", "Ca3Zn", "CdHg2", "Mg3Cd", "MgCd3", "ZnCdPt2", "ScCd3", "TiFe", "Ti2Cd", "V5Sb4", "Sc2Co", "Hf2Cu", "Cu4Pd", "CuSnRh2", "Ti2Cu3", "Mg2Hg", "ScHg3", "YHg2", "YHg3", "Mg3Ir", "IrW", "Ir3W", "YIr", "LiPt2", "LiPt7", "Li5Sn2", "Li7Sn2", "Li7Sn3", "Li13Sn5", "MgPt3", "Mg5Rh2", "Mg2Zn11", "MoRh3", "SnMo3", "NbZn2", "Li2AlPd", "LiAl2Pd", "Li2AlPt", "LiAl2Pt", "Li2AlRh", "LiAl2Rh", "TaPd2", "TaPd3", "Ti2Pd3", "Sn3Pt2", "TaPt2", "TaPt3", "Ti3Pt5", "TiPt8", "ZnPt3", "Rh3W", "ScRu", "Ta3Sn", "Ti2Sn", "TiZn2", 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"gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Linear regression" }, "xaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "DFT (MP) bulk modulus (GPa)" }, "type": "linear" }, "yaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Predicted bulk modulus (GPa)" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from figrecipes import PlotlyFig\n", "from sklearn.model_selection import cross_val_predict\n", "\n", "pf = PlotlyFig(x_title='DFT (MP) bulk modulus (GPa)',\n", " y_title='Predicted bulk modulus (GPa)',\n", " title='Linear regression',\n", " mode='notebook',\n", " filename=\"lr_regression.html\")\n", "\n", "pf.xy(xy_pairs=[(y, cross_val_predict(lr, X, y, cv=crossvalidation)), ([0, 400], [0, 400])], \n", " labels=df['formula'], \n", " modes=['markers', 'lines'],\n", " lines=[{}, {'color': 'black', 'dash': 'dash'}], \n", " showlegends=False\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not too bad! However, there are definitely some outliers (you can hover over the points with your mouse to see what they are). We will see below (with a random forest model) how the accuracy changes when we try the model on a completely new test data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Try a random forest model\n", "\n", "Let's see if a more complex machine learning model does better. We can try a random forest model which is a good \"starting\" machine learning model, although one can usually do better. Let's repeat the steps for linear regression but for a random forest model." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "training R2 = 0.989\n", "training RMSE = 7.687\n" ] } ], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "\n", "rf = RandomForestRegressor(n_estimators=50, random_state=1)\n", "\n", "rf.fit(X, y)\n", "print('training R2 = ' + str(round(rf.score(X, y), 3)))\n", "print('training RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y, y_pred=rf.predict(X))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At least on the training data, we have very low RMSE and very high R2 - this is good! But let's see if these numbers hold up on cross-validation." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cross-validation results:\n", "Folds: 10, mean R2: 0.924\n", "Folds: 10, mean RMSE: 19.277\n" ] } ], "source": [ "# compute cross validation scores for random forest model\n", "r2_scores = cross_val_score(rf, X, y, scoring='r2', cv=crossvalidation, n_jobs=-1)\n", "scores = cross_val_score(rf, X, y, scoring='neg_mean_squared_error', cv=crossvalidation, n_jobs=-1)\n", "rmse_scores = [np.sqrt(abs(s)) for s in scores]\n", "\n", "print('Cross-validation results:')\n", "print('Folds: %i, mean R2: %.3f' % (len(scores), np.mean(np.abs(r2_scores))))\n", "print('Folds: %i, mean RMSE: %.3f' % (len(scores), np.mean(np.abs(rmse_scores))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like upon cross-validation, we do slightly better than a linear regression but not *too* much better. Let's plot this one as well." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "hoverinfo": "x+y+text", "hoverlabel": { "font": { "family": "Courier", "size": 25 } }, "marker": { "colorscale": [ [ 0, "#440154" ], [ 0.1111111111111111, "#482878" ], [ 0.2222222222222222, "#3e4989" ], [ 0.3333333333333333, "#31688e" ], [ 0.4444444444444444, "#26828e" ], [ 0.5555555555555556, "#1f9e89" ], [ 0.6666666666666666, "#35b779" ], [ 0.7777777777777778, "#6ece58" ], [ 0.8888888888888888, "#b5de2b" ], [ 1, "#fde725" ] ], "line": { "color": "black", "width": 1 }, "showscale": false, "size": 10, "symbol": "circle" }, "mode": "markers", "showlegend": false, "text": [ "Nb4CoSi", "Al(CoSi)2", "SiOs", 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"Li2Pd", "Cr3Si", "Mg3Hg", "GeO2", "Y3Pt", "Li(YSi)2", "Ca(SiAu)2", "Sb2Au", "Rh", "Ti2Cu", "Ca(ZnSb)2", "Ca(CdSb)2", "LiSiCu2", "Nb", "Cr5Si3", "ZnSb", "Hf(MnSn)6", "CoSb2", "Nb5SiSn2", "SbRu", "CrSi", "CoSi", "Mn11Pd21", "Sr", "SiC", "Ca(AlSi)2", "MnAl", "MgPd3", "Sc5Si3", "TaCo3", "TiB", "MnSb", "Zn", "ReSi", "LiSi", "Li3Sb", "Re", "Mo3Os", "GaN", "SiC", "YSiCu", "ScAl2", "SiRh", "HfCr2", "Tl", "TiCo", "AlPd", "CaPd2", "CaSi2", "V3Au", "Li2O2", "CaPt2", "Hf2Al3", "Hf3Al2", "ZnO2", "CaSbPt", "In", "Ag", "Te4Mo3", "CaSi2", "TiFeSi", "TaAl3", "Be", "FeSi", "VPd3", "AlOs", "CaSiPd", "Ga2O3", "AlP", "AlAs", "GaP", "ScPt", "Si2Mo", "Si2W", "ZnPt", "CaSiPt", "CaSiPt", "Sc3RuC4", "Cr", "ScSiAu", "YSiAu", "W", "NbC", "YCd", "Y2Al3Si2", "YRh2", "CoPt3", "ScSiPt", "Hg4Pt", "GeTe", "Cd", "Y4C5", "CoPt", "Sr", "MoPt2", "NbZn3", "ScMnSi", "Li2Sb", "LiBeSb", "Ca3(AlSi)2", "K2O", "SrF2", "CoSb2", "BN", "Si3N4", "Sc2CoSi2", "NbCrSi", "LiZnSb", "Hf2Si", "Ti2CdC", "ScSi", "YSi", "Al2Cu", "VCu3Se4" ], 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"white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Random forest regression" }, "xaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "DFT (MP) bulk modulus (GPa)" }, "type": "linear" }, "yaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Random forest bulk modulus (GPa)" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from figrecipes import PlotlyFig\n", "\n", "pf_rf = PlotlyFig(x_title='DFT (MP) bulk modulus (GPa)',\n", " y_title='Random forest bulk modulus (GPa)',\n", " title='Random forest regression',\n", " mode='notebook',\n", " filename=\"rf_regression.html\")\n", "\n", "pf_rf.xy([(y, cross_val_predict(rf, X, y, cv=crossvalidation)), ([0, 400], [0, 400])], \n", " labels=df['formula'], modes=['markers', 'lines'],\n", " lines=[{}, {'color': 'black', 'dash': 'dash'}], showlegends=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visually, this looks a little better but not *that* much better. The random forest did very well in training, but is only a little better than linear regression when we plot the cross-validation error as per above.\n", "\n", "You could (optionally) visualize the *training* error by replacing the code ``cross_val_predict(rf, X, y, cv=crossvalidation)`` in the above cell with ``rf.predict(X)``. That would look a lot better, but would not be an accurate representation of your prediction error." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "training R2 = 0.987\n", "training RMSE = 8.259\n", "test R2 = 0.942\n", "test RMSE = 16.928\n" ] } ], "source": [ "from sklearn.model_selection import train_test_split\n", "X['formula'] = df['formula']\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)\n", "train_formula = X_train['formula']\n", "X_train = X_train.drop('formula', axis=1)\n", "test_formula = X_test['formula']\n", "X_test = X_test.drop('formula', axis=1)\n", "\n", "rf_reg = RandomForestRegressor(n_estimators=50, random_state=1)\n", "rf_reg.fit(X_train, y_train)\n", "\n", "# get fit statistics\n", "print('training R2 = ' + str(round(rf_reg.score(X_train, y_train), 3)))\n", "print('training RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y_train, y_pred=rf_reg.predict(X_train))))\n", "print('test R2 = ' + str(round(rf_reg.score(X_test, y_test), 3)))\n", "print('test RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y_test, y_pred=rf_reg.predict(X_test))))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "histnorm": "probability", "hoverinfo": "x+y+text", "hoverlabel": { "font": { "family": "Courier", "size": 25 } }, "marker": { "color": "blue" }, "name": "train", "opacity": 0.7, "type": "histogram", "x": [ 4.8155234826598985, 0.042680126655980644, -5.715583533739931, -2.1635422045732113, -4.743323655516036, 0.49561867695602757, 8.149994982879946, -0.5771314705800137, -15.493589394959983, -1.1134926149939943, 1.870787097251963, 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"" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Random forest regression residuals" }, "xaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Bulk modulus prediction residual (GPa)" }, "type": "linear" }, "yaxis": { "tickfont": { "family": "Courier", "size": 25 }, "title": { "font": { "family": "Courier", "size": 25 }, "text": "Probability" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from figrecipes import PlotlyFig\n", "pf_rf = PlotlyFig(x_title='Bulk modulus prediction residual (GPa)',\n", " y_title='Probability',\n", " title='Random forest regression residuals',\n", " mode=\"notebook\",\n", " filename=\"rf_regression_residuals.html\")\n", "\n", "hist_plot = pf_rf.histogram(data=[y_train-rf_reg.predict(X_train), \n", " y_test-rf_reg.predict(X_test)],\n", " histnorm='probability', colors=['blue', 'red'],\n", " return_plot=True\n", " )\n", "hist_plot[\"data\"][0]['name'] = 'train'\n", "hist_plot[\"data\"][1]['name'] = 'test'\n", "pf_rf.create_plot(hist_plot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's see what are the most important features used by the random forest model." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { 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20 }, "title": { "font": { "family": "Courier", "size": 20 }, "text": "" } }, "yaxis": { "tickfont": { "family": "Courier", "size": 20 }, "title": { "font": { "family": "Courier", "size": 20 }, "text": "Importance (%)" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "importances = rf.feature_importances_\n", "# included = np.asarray(included)\n", "included = X.columns.values\n", "indices = np.argsort(importances)[::-1]\n", "\n", "pf = PlotlyFig(y_title='Importance (%)',\n", " title='Feature by importances',\n", " mode='notebook',\n", " fontsize=20,\n", " ticksize=15)\n", "\n", "pf.bar(x=included[indices][0:10], y=importances[indices][0:10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Features relating to the melting point and to the volume per atom / density are the most important in the random forest model.\n", "\n", "This concludes the tutorial! You are now familiar with some of the basic features of matminer." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }