test_tabular_torch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from permanova.experiments.exp_utils import TorchTest as tt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PERMANOVA test on tabular Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are presented a series of experiments on tabular data with continuous variables. The tests are handled on different levels of noise applied to the second sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normally distributed covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two covariates - low noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 12/10000 [00:00<01:31, 109.07it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:10<00:00, 916.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.9557\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_normal_covariates(\n",
    "    dim=2, noise_mean=0, noise_std=1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two covariates - high noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:03<00:00, 2802.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.0001\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_normal_covariates(\n",
    "    dim=2, noise_mean=1, noise_std=1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple covariates - low noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:09<00:00, 1015.70it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 1.0\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_normal_covariates(\n",
    "    dim=10, noise_mean=0, noise_std=1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple covariates - high noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:10<00:00, 977.34it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.0001\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_normal_covariates(\n",
    "    dim=10, noise_mean=1, noise_std=1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixture of gaussians covariates - low noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two covariates - low noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:04<00:00, 2418.24it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.39396\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_mixture_covariates(\n",
    "    dim=2, noise_mean_perc=0.01, noise_std_perc=0.01, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two covariates - high noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:03<00:00, 2543.15it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.0001\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_mixture_covariates(\n",
    "    dim=2, noise_mean_perc=0.1, noise_std_perc=0.1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple covariates - low noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:10<00:00, 930.26it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.32967\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_mixture_covariates(\n",
    "    dim=10, noise_mean_perc=0.01, noise_std_perc=0.01, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple covariates - high noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing permutations...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/10000 [00:00<?, ?it/s]d:\\Projects\\light_permanova\\venv\\Lib\\site-packages\\torch\\storage.py:414: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature.\n",
      "  return torch.load(io.BytesIO(b))\n",
      "100%|██████████| 10000/10000 [00:10<00:00, 938.08it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.0001\n"
     ]
    }
   ],
   "source": [
    "sample_1, sample_2 = tt.generate_samples_with_mixture_covariates(\n",
    "    dim=10, noise_mean_perc=0.1, noise_std_perc=0.1, size=10000\n",
    ")\n",
    "tt.test(sample_1, sample_2, show_plots=False)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "myenv",
   "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": "3.12.5"
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 },
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