doc/analyses_from_paper/sample_size_calculator.ipynb

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    "# Sample size calculator"
   ]
  },
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    "We develop a sample size calculator for CCA and PLS. We had previously generated datasets for a variety of parameters and determined the corresponding required sample sizes to bound statistical power and error metrics. To circumvent the computational cost associated with this approach for parameters that we had not simulated, we interpolate the parameter dependencies, by fitting a suitable linear model."
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   "source": [
    "## Setup"
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       "       style='height:15px; border-radius:12px; display: inline-block; float: left'></img>\n",
       "  \n",
       "\n",
       "\n",
       "</div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "import scipy.linalg\n",
    "import scipy.stats\n",
    "from scipy.stats import pearsonr, zscore\n",
    "from scipy.spatial.distance import pdist, cdist, squareform\n",
    "\n",
    "from sklearn import clone\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import cross_validate, KFold, ShuffleSplit\n",
    "\n",
    "from gemmr.data import load_outcomes, print_ds_stats\n",
    "from gemmr.metrics import *\n",
    "from gemmr.sample_size import *\n",
    "from gemmr.sample_size.linear_model import prep_data_for_lm, do_fit_lm\n",
    "from gemmr.util import subset_ds\n",
    "\n",
    "import matplotlib\n",
    "import holoviews as hv\n",
    "from holoviews import opts\n",
    "hv.extension('matplotlib')\n",
    "hv.renderer('matplotlib').param.set_param(dpi=120)\n",
    "\n",
    "from my_config import *\n",
    "\n",
    "import warnings\n",
    "from matplotlib import MatplotlibDeprecationWarning\n",
    "warnings.simplefilter('ignore', MatplotlibDeprecationWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading data from subfolder 'gemmr_latest'\n",
      "Loading data from subfolder 'gemmr_latest'\n"
     ]
    }
   ],
   "source": [
    "data_home = None\n",
    "ds_cca = load_outcomes('sweep_cca_cca_random_sum+-3+0_wOtherModel', model='cca', add_prefix='cca_', data_home=data_home).sel(mode=0)\n",
    "ds_pls = load_outcomes('sweep_pls_pls_random_sum+-3+0_wOtherModel', model='pls', add_prefix='pls_', data_home=data_home).sel(mode=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ds_cca = ds_cca.sel(px=ds_cca.px < 128)\n",
    "ds_pls = ds_pls.sel(px=ds_pls.px < 128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ds_cca = subset_ds(ds_cca, n_keep=25, keyvar='cca_between_assocs')\n",
    "ds_pls = subset_ds(ds_pls, n_keep=25, keyvar='pls_between_assocs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What's in the outcome data files?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_rep\t\t 100\n",
      "n_per_ftr\t [   3    4    8   16   32   64  128  256  512 1024 2048 4096 8192]\n",
      "r\t\t [0.1 0.3 0.5 0.7]\n",
      "px\t\t [ 2  4  8 16 32 64]\n",
      "ax+ay range\t(-2.97, -0.10)\n",
      "py\t\t== px\n",
      "\n",
      "<xarray.DataArray 'n_Sigmas' (px: 6, r: 4)>\n",
      "array([[25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [ 0, 25, 25, 25]])\n",
      "Coordinates:\n",
      "  * r        (r) float64 0.1 0.3 0.5 0.7\n",
      "  * px       (px) int64 2 4 8 16 32 64\n",
      "\n",
      "power\t\tcalculated\n"
     ]
    }
   ],
   "source": [
    "print_ds_stats(ds_cca, prefix='cca_')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_rep\t\t 100\n",
      "n_per_ftr\t [   3    4    8   16   32   64  128  256  512 1024 2048 4096 8192]\n",
      "r\t\t [0.1 0.3 0.5 0.7]\n",
      "px\t\t [ 2  4  8 16 32 64]\n",
      "ax+ay range\t(-2.97, -0.10)\n",
      "py\t\t== px\n",
      "\n",
      "<xarray.DataArray 'n_Sigmas' (px: 6, r: 4)>\n",
      "array([[25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [25, 25, 25, 25],\n",
      "       [ 0, 25, 25, 25],\n",
      "       [ 0, 25, 25, 25],\n",
      "       [ 0,  0,  0, 21]])\n",
      "Coordinates:\n",
      "  * r        (r) float64 0.1 0.3 0.5 0.7\n",
      "  * px       (px) int64 2 4 8 16 32 64\n",
      "\n",
      "power\t\tcalculated\n"
     ]
    }
   ],
   "source": [
    "print_ds_stats(ds_pls, prefix='pls_')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit a linear model to log(required sample size) to predict sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_linear_model(\n",
    "    _ds, \n",
    "    cv=KFold(2),\n",
    "    include_pdiff=False,\n",
    "    include_pc_var_decay_constants=True,\n",
    "    include_latent_explained_vars=True,\n",
    "    prefix=''\n",
    "):\n",
    "    \n",
    "    r_squareds, error_bars, true_ys, predicted_ys = {}, {}, {}, {}\n",
    "    \n",
    "    n_reqs_per_ftr = calc_n_required_all_metrics(_ds, target_power=0.9, target_error=0.1, search_dim='n_per_ftr', prefix=prefix)\n",
    "    \n",
    "    for metric_label, n_req_per_ftr in n_reqs_per_ftr.items():\n",
    "        \n",
    "        n_req = n_req_per_ftr * (_ds.px + _ds.py)\n",
    "        \n",
    "        lm, X, y, coeff_names = do_fit_lm(\n",
    "            _ds, n_req, \n",
    "            include_pdiff=include_pdiff,\n",
    "            include_pc_var_decay_constants=include_pc_var_decay_constants,\n",
    "            include_latent_explained_vars=include_latent_explained_vars,\n",
    "            prefix=prefix\n",
    "        )\n",
    "\n",
    "        r_squareds[metric_label] = lm.score(X, y)\n",
    "\n",
    "        # make error_bar estimates through CV\n",
    "        cres = cross_validate(lm, X, y, \n",
    "                              cv=ShuffleSplit(100, test_size=0.5, random_state=42), \n",
    "                              return_estimator=True)\n",
    "\n",
    "        coefs = np.r_[[lm.intercept_], lm.coef_].reshape(1, -1)\n",
    "        qs = (.025, .975)\n",
    "        cv_cis = np.quantile(\n",
    "            np.asarray([np.r_[[estr.intercept_], estr.coef_] for estr in cres['estimator']]),\n",
    "            qs,\n",
    "            axis=0\n",
    "        )\n",
    "\n",
    "        error_bars[metric_label] = np.concatenate([\n",
    "            np.arange(1 + X.shape[1]).reshape(1, -1),\n",
    "            coefs,\n",
    "            cv_cis - coefs\n",
    "        ], axis=0).T\n",
    "\n",
    "        median_minus_log_r_true = np.median(X[:, 0])\n",
    "        masks = [\n",
    "            X[:, 0] <= median_minus_log_r_true,\n",
    "            X[:, 0] > median_minus_log_r_true,\n",
    "        ]\n",
    "\n",
    "        assert np.all(masks[0] | masks[1])\n",
    "        \n",
    "        _true_ys, _predicted_ys = [], []\n",
    "        for mask in masks:\n",
    "            \n",
    "            train, test = mask, ~mask\n",
    "            \n",
    "            # make sure there's no overlap in the -log(r) values of train and test set\n",
    "            assert len(set(X[train, 0].tolist()).intersection(X[test, 0].tolist())) == 0\n",
    "            \n",
    "            _lm = clone(lm).fit(X[train], y[train])\n",
    "            _true_ys.append(y[test])\n",
    "            _predicted_ys.append(lm.predict(X[test]))\n",
    "\n",
    "        true_ys[metric_label] = np.hstack(_true_ys)\n",
    "        predicted_ys[metric_label] = np.hstack(_predicted_ys)\n",
    "        \n",
    "    return r_squareds, error_bars, true_ys, predicted_ys, coeff_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# due to high loading-error for px < 5:\n",
    "# make linear model only for px >= 5\n",
    "r_squareds_cca, error_bars_cca, true_ys_cca, predicted_ys_cca, coeff_names_cca = run_linear_model(\n",
    "    ds_cca.sel(px=ds_cca.px>4),\n",
    "    include_pdiff=False,\n",
    "    include_pc_var_decay_constants=True,\n",
    "    include_latent_explained_vars=False,  # <- deprecated, doesn't exist any more\n",
    "    prefix='cca_'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# due to high loading-error for px < 5:\n",
    "# make linear model only for px >= 5\n",
    "r_squareds_pls, error_bars_pls, true_ys_pls, predicted_ys_pls, coeff_names_pls = run_linear_model(\n",
    "    ds_pls.sel(px=ds_pls.px>4),\n",
    "    include_pdiff=False,\n",
    "    include_pc_var_decay_constants=True,\n",
    "    include_latent_explained_vars=False,  # <- deprecated, doesn't exist any more\n",
    "    prefix='pls_'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear model coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lm_coeffs(\n",
    "    error_bars,\n",
    "    r_squareds,\n",
    "    coeff_names,\n",
    "    metrics=None,\n",
    "    plot_error_bars=True,\n",
    "    label='',\n",
    "    color=None,\n",
    "):\n",
    "    \n",
    "    def x_ticks_format_variable_name(x):\n",
    "        int_x = int(x)\n",
    "        if (x == int_x) and (x < len(coeff_names)):\n",
    "            return coeff_names[int(x)]\n",
    "        else:\n",
    "            return ''\n",
    "        \n",
    "    predictor_variable_dim = hv.Dimension('predictor_variable', label='Predictor variable',\n",
    "                                          value_format=x_ticks_format_variable_name\n",
    "                                         )\n",
    "\n",
    "    markers = ['s', 'o', 'd', 'v', 'x', '.']\n",
    "    \n",
    "    if metrics is None:\n",
    "        metrics = list(error_bars.keys())\n",
    "    \n",
    "    panel_lm_coeffs = hv.Overlay()\n",
    "    for metric_i, metric_label in enumerate(metrics):\n",
    "        \n",
    "        if plot_error_bars:\n",
    "            panel_lm_coeffs *= hv.ErrorBars(\n",
    "                error_bars[metric_label], \n",
    "                kdims=predictor_variable_dim,\n",
    "            ) \n",
    "        \n",
    "        panel_lm_coeffs *= hv.Scatter(\n",
    "            (error_bars[metric_label][:, 0], error_bars[metric_label][:, 1]),\n",
    "            kdims=predictor_variable_dim,\n",
    "            label=label,\n",
    "        ).opts(marker=markers[metric_i])\n",
    "        \n",
    "    if color is None:\n",
    "        color = hv.Cycle(metric_clrs_li)\n",
    "        \n",
    "    panel_lm_coeffs = panel_lm_coeffs.redim(\n",
    "            y='Coefficient value'\n",
    "        ).opts(\n",
    "            opts.ErrorBars(ylim=(None, None), padding=0.05),\n",
    "            opts.Scatter(color=color, s=40),\n",
    "            opts.Text(color=color),\n",
    "            opts.HLine(color='black', linewidth=.1, linestyle='--'),\n",
    "            opts.Overlay(xrotation=45, xticks=np.arange(len(coeff_names), dtype=int).tolist()),\n",
    "        )\n",
    "    return panel_lm_coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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' style='max-width:100%; margin: auto; display: block; '/>"
      ],
      "text/plain": [
       ":Overlay\n",
       "   .Scatter.PLS :Scatter   [predictor_variable]   (Coefficient value)\n",
       "   .Scatter.CCA :Scatter   [predictor_variable]   (Coefficient value)\n",
       "   .Text.I      :Text   [x,y]\n",
       "   .Text.II     :Text   [x,y]"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panel_lm_coeffs_max = (\n",
    "    plot_lm_coeffs(error_bars_pls, r_squareds_pls, coeff_names_pls, metrics=['combined'], plot_error_bars=False, label='PLS', color=clr_pls)\n",
    "    * plot_lm_coeffs(error_bars_cca, r_squareds_cca, coeff_names_cca, metrics=['combined'], plot_error_bars=False, label='CCA', color=clr_cca)\n",
    "    * hv.Text(3.1, 2.5, 'CCA', halign='right', valign='top', fontsize=7).opts(color=clr_cca)\n",
    "    * hv.Text(3.1, 2.2, 'PLS', halign='right', valign='top', fontsize=7).opts(color=clr_pls)\n",
    ").opts(*fig_opts).opts(\n",
    "    opts.Overlay(show_legend=False, padding=.1, ylim=(-.3, None), fig_inches=(1.7, None)),\n",
    ")\n",
    "panel_lm_coeffs_max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear model prediction errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scatter_lm_predictions(\n",
    "    true_ys,\n",
    "    predicted_ys,\n",
    "    metric_label\n",
    "):\n",
    "    \n",
    "    true_ys = np.exp(true_ys[metric_label])\n",
    "    predicted_ys = np.exp(predicted_ys[metric_label])\n",
    "    \n",
    "    mn = min(true_ys.min(), predicted_ys.min())\n",
    "    mx = max(true_ys.max(), predicted_ys.max())\n",
    "    \n",
    "    panel_n_crit_lm_predictions = (\n",
    "        hv.Scatter(\n",
    "            (true_ys, predicted_ys)\n",
    "        ) * hv.Curve(\n",
    "            ([mn, mx], [mn, mx])\n",
    "        )\n",
    "    ).redim(\n",
    "        x='True req. sample size',\n",
    "        y='Out-of-sample prediction'\n",
    "    ).opts(\n",
    "        opts.Curve(color='black', linestyle='--', linewidth=1),\n",
    "        opts.Scatter(s=3),\n",
    "    )\n",
    "    return panel_n_crit_lm_predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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' style='max-width:100%; margin: auto; display: block; '/>"
      ],
      "text/plain": [
       ":Overlay\n",
       "   .Scatter.I :Scatter   [True req. sample size]   (Out-of-sample prediction)\n",
       "   .Curve.I   :Curve   [True req. sample size]   (Out-of-sample prediction)"
      ]
     },
     "execution_count": 13,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panel_cca_n_req_lm_predictions = scatter_lm_predictions(true_ys_cca, predicted_ys_cca, 'combined').opts(\n",
    "    opts.Scatter(color=clr_cca),\n",
    "    opts.Overlay(logx=True, logy=True)\n",
    ").opts(*fig_opts).opts(fig_inches=(1.7, None))\n",
    "panel_cca_n_req_lm_predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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' style='max-width:100%; margin: auto; display: block; '/>"
      ],
      "text/plain": [
       ":Overlay\n",
       "   .Scatter.I :Scatter   [True req. sample size]   (Out-of-sample prediction)\n",
       "   .Curve.I   :Curve   [True req. sample size]   (Out-of-sample prediction)"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panel_pls_n_req_lm_predictions = scatter_lm_predictions(true_ys_pls, predicted_ys_pls, 'combined'\n",
    ").opts(\n",
    "    opts.Scatter(color=clr_pls),\n",
    "    opts.Overlay(logx=True, logy=True)\n",
    ").opts(*fig_opts).opts(fig_inches=(1.7, None))\n",
    "\n",
    "panel_pls_n_req_lm_predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict correlations with linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_req_corrs(\n",
    "    ds, metric='combined',         \n",
    "    include_pc_var_decay_constants=False,\n",
    "    prefix=''\n",
    "):\n",
    "    \n",
    "    n_req_per_ftr = calc_n_required_all_metrics(ds, search_dim='n_per_ftr', prefix=prefix)[metric]\n",
    "    n_req = n_req_per_ftr * (ds.px + ds.py)\n",
    "\n",
    "    r_lists = [[.1, .3], [.5, .7]]\n",
    "    true_rs, predicted_rs = [], []\n",
    "    for r_list in r_lists:\n",
    "        lm, X, y, coeff_names = do_fit_lm(ds.sel(r=r_list), n_req.sel(r=r_list), include_pdiff=False,\n",
    "                                                 include_pc_var_decay_constants=include_pc_var_decay_constants,\n",
    "                                                 include_latent_explained_vars=False,\n",
    "                                                 prefix=prefix,\n",
    "                                                )\n",
    "        \n",
    "        intercept = lm.intercept_\n",
    "        coefs = lm.coef_\n",
    "        \n",
    "        other_rs = [r for r in ds.r.values if r not in r_list]\n",
    "        Xtest, ytest, coeff_names_test = prep_data_for_lm(ds.sel(r=other_rs), n_req.sel(r=other_rs), include_pdiff=False,\n",
    "                                                          include_pc_var_decay_constants=include_pc_var_decay_constants,\n",
    "                                                          include_latent_explained_vars=False,\n",
    "                                                          prefix=prefix,\n",
    "                                                         )\n",
    "        \n",
    "        # double check that first column of X contains -np.log(r)\n",
    "        for rr in -np.log(np.asarray(other_rs)):\n",
    "            assert rr in Xtest[:, 0]\n",
    "        \n",
    "        true_rs.append(np.exp(-Xtest[:, 0]))\n",
    "        \n",
    "        if not include_pc_var_decay_constants:\n",
    "            predicted_rs.append(\n",
    "                np.exp((- ytest + intercept + Xtest[:, 1] * coefs[1]) / coefs[0])\n",
    "            )\n",
    "        else:\n",
    "            predicted_rs.append(\n",
    "                np.exp((- ytest + intercept + Xtest[:, 1] * coefs[1] + Xtest[:, 2] * coefs[2]) / coefs[0])\n",
    "            )\n",
    "    true_rs = np.hstack(true_rs)\n",
    "    predicted_rs = np.hstack(predicted_rs)\n",
    "        \n",
    "    \n",
    "    return true_rs, predicted_rs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "cca_rs_true, cca_rs_predicted  = predict_req_corrs(ds_cca, prefix='cca_')\n",
    "pls_rs_true, pls_rs_predicted  = predict_req_corrs(ds_pls, prefix='pls_', include_pc_var_decay_constants=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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' style='max-width:100%; margin: auto; display: block; '/>"
      ],
      "text/plain": [
       ":Layout\n",
       "   .Scatter.CCA :Scatter   [True correlation]   (Out-of-sample prediction\n",
       "with linear model)\n",
       "   .Scatter.PLS :Scatter   [True correlation]   (Out-of-sample prediction\n",
       "with linear model)"
      ]
     },
     "execution_count": 17,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_predicted_req_corrs = (\n",
    "    hv.Scatter(\n",
    "        (cca_rs_true, cca_rs_predicted),\n",
    "        kdims='true',\n",
    "        vdims='predicted',\n",
    "        label='CCA'\n",
    "    ).opts(sublabel_format='e')\n",
    "    +  hv.Scatter(\n",
    "        (pls_rs_true, pls_rs_predicted),\n",
    "        kdims='true',\n",
    "        vdims='predicted',\n",
    "        label='PLS'\n",
    "    ).opts(ylabel='', sublabel_format='f')\n",
    ").redim(\n",
    "    true='True correlation',\n",
    "    predicted='Out-of-sample prediction\\nwith linear model'\n",
    ").opts(*fig_opts).opts(\n",
    "    opts.Scatter(s=10, xlim=(0, 1), ylim=(0, None)),\n",
    "    opts.Layout(sublabel_position=(-.45, .95))\n",
    ")\n",
    "\n",
    "fig_predicted_req_corrs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:param.LayoutPlot06878: :Overlay is empty, skipping subplot.\n",
      "WARNING:param.LayoutPlot07136: :Overlay is empty, skipping subplot.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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' style='max-width:100%; margin: auto; display: block; '/>"
      ],
      "text/plain": [
       ":Layout\n",
       "   .Overlay.I                         :Overlay\n",
       "   .Overlay.Linear_model_coefficients :Overlay\n",
       "      .Scatter.PLS :Scatter   [predictor_variable]   (Coefficient value)\n",
       "      .Scatter.CCA :Scatter   [predictor_variable]   (Coefficient value)\n",
       "      .Text.I      :Text   [x,y]\n",
       "      .Text.II     :Text   [x,y]\n",
       "   .Overlay.CCA                       :Overlay\n",
       "      .Scatter.I :Scatter   [True req. sample size]   (Out-of-sample prediction)\n",
       "      .Curve.I   :Curve   [True req. sample size]   (Out-of-sample prediction)\n",
       "   .Overlay.PLS                       :Overlay\n",
       "      .Scatter.I :Scatter   [True req. sample size]   (Out-of-sample prediction)\n",
       "      .Curve.I   :Curve   [True req. sample size]   (Out-of-sample prediction)\n",
       "   .Scatter.CCA                       :Scatter   [True correlation]   (Out-of-sample prediction\n",
       "with linear model)\n",
       "   .Scatter.PLS                       :Scatter   [True correlation]   (Out-of-sample prediction\n",
       "with linear model)"
      ]
     },
     "execution_count": 18,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = (\n",
    "    hv.Overlay()\n",
    "    + panel_lm_coeffs_max.relabel('Linear model coefficients').opts(xticks=4, xrotation=25, sublabel_format='b')\n",
    "    + panel_cca_n_req_lm_predictions.relabel('CCA').opts(sublabel_format='c')\n",
    "    + panel_pls_n_req_lm_predictions.relabel('PLS').opts(sublabel_format='d')\n",
    "    # +  panel_pls_n_req_lm_predictions_wLatentExplVar.relabel('PLS w/ additional\\nunobservable predictor')\n",
    "    + fig_predicted_req_corrs\n",
    ").cols(\n",
    "    2\n",
    ").opts(*fig_opts).opts(\n",
    "    opts.Layout(vspace=.75, sublabel_position=(-.4, 1))\n",
    ")\n",
    "\n",
    "hv.save(fig, 'fig/figS_sample_size_calculator.pdf')\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Usage of linear models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gemmr import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.1: 189701, 0.3: 17211, 0.5: 5638}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cca_sample_size(100, 50, -1, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a dictionary with keys indicating assumed ground truth correlations and values giving the corresponding sample size estimates. For PLS, in addition to the number of features in each set, the powerlaw decay constants for the within-set principal component spectra need to be specified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.1: 18459, 0.3: 2949, 0.5: 1257}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pls_sample_size(10, 10, -1, -1)"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "353a147e3613e6b917b871b1c7403ff166c02a1998fca17dbe62e70053517a56"
  },
  "kernelspec": {
   "display_name": "Python 3.7.7 64-bit ('gemmr': conda)",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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