{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import time\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pyblip"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In many applications, we can tell that a signal of interest exists but cannot perfectly \"localize\" it. For example, when regressing an outcome $Y$ on highly correlated covariates $(X_1, X_2)$, the data may suggest that *at least* one of $(X_1, X_2)$ influences $Y$, but it may be challenging to tell which of $(X_1, X_2)$ is important. Likewise, in genetic fine-mapping, biologists may have high confidence that a gene influences a disease without knowing precisely which genetic variants cause the disease. Similar problems arise in many settings with spatial or temporal structure, including change-point detection and astronomical point-source detection.\n",
    "\n",
    "*Bayesian Linear Programming* (BLiP) is a method which jointly detects as many signals as possible while localizing them as precisely as possible. BLiP can wrap on top of nearly any Bayesian model or algorithm, and it will return a set of regions which each contain at least one signal with high confidence. For example, in regression problems, BLiP might return the region $(X_1, X_2)$, which suggests that at least one of $(X_1, X_2)$ is an important variable. BLiP controls the false discovery rate while also making these regions as narrow as possible, meaning that (roughly speaking) it will perfectly localize signals whenever this is possible! See [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208) for more details.\n",
    "\n",
    "``pyblip`` is an efficient python implementation of BLiP, which is designed so that BLiP can wrap on top of the Bayesian model in only one or two lines of code. Below, we give concrete examples of how to apply ``pyblip`` in three settings: variable selection, change-point detection, and point-source detection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Variable selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Generating synthetic data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we generate synthetic data of highly correlated covariates $X = (X_1, \\dots, X_p)$ and a response $Y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate synthetic data with 10 signal variables\n",
    "np.random.seed(12345)\n",
    "X, y, beta = pyblip.utilities.generate_regression_data(\n",
    "    n=300, p=500, k=5, sparsity=0.02, dgp_seed=12345\n",
    ")\n",
    "signal_variables = np.where(beta != 0)[0]\n",
    "# X has strong local correlations\n",
    "sns.heatmap(np.corrcoef(X.T), cmap='RdBu', center=0)\n",
    "plt.title('Correlation matrix for X')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Linear Spike-and-Slab model + BLiP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply BLiP in two steps. First, we fit a Bayesian model to $(X, Y)$---in this case, we use a spike-and-slab model for sparse linear regression. Second, we run BLiP directly on top of the posterior samples from the Bayesian model, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: sample from Gaussian spike-and-slab model\n",
    "lm = pyblip.linear.LinearSpikeSlab(X=X, y=y)\n",
    "lm.sample(N=2000, chains=5, burn=200, bsize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "BLiP ran in 0.96 seconds.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Step 2: Apply BLiP to detect signal variables\n",
    "t0 = time.time()\n",
    "detections = pyblip.blip.BLiP(\n",
    "    samples=lm.betas,\n",
    "    q=0.1,\n",
    "    error='fdr',\n",
    "    verbose=False,\n",
    ")\n",
    "print(f\"\\nBLiP ran in {np.around(time.time() - t0, 2)} seconds.\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the data is synthetic, we can check whether the results from BLiP are accurate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The true signal variables are [ 54  68 148 184 272 306 383 409 426 471].\n",
      "BLiP correctly detected a signal variable in {54}.\n",
      "BLiP correctly detected a signal variable in {68}.\n",
      "BLiP correctly detected a signal variable in {184}.\n",
      "BLiP correctly detected a signal variable in {272}.\n",
      "BLiP correctly detected a signal variable in {306}.\n",
      "BLiP correctly detected a signal variable in {383}.\n",
      "BLiP correctly detected a signal variable in {426}.\n",
      "BLiP correctly detected a signal variable in {417, 421, 404, 407, 408, 409, 411, 412}.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The true signal variables are {signal_variables}.\")\n",
    "for x in detections:\n",
    "    true_detection = len(x.group.intersection(set(signal_variables))) > 0\n",
    "    if true_detection:\n",
    "        print(f\"BLiP correctly detected a signal variable in {x.group}.\")\n",
    "    else:\n",
    "        print(f\"BLiP incorrectly detected a signal variable in {x.group}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, sometimes BLiP will detect individual signal variables, but often this is not possible due to the high correlations among $X$. In the latter case, BLiP outputs larger clusters of variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 SuSiE + BLiP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BLiP can apply on top of nearly any Bayesian model or algorithm, including variational algorithms. Here, we show how to apply BLiP on top of a SuSiE model [(Wang et al, 2020)](https://www.biorxiv.org/content/10.1101/501114v4). We do this in three steps: Step 1 is to fit SuSiE, Step 2 is to create candidate groups based off of the SuSiE outputs, and Step 3 is to apply BLiP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rpy2.ipython extension is already loaded. To reload it, use:\n",
      "  %reload_ext rpy2.ipython\n"
     ]
    }
   ],
   "source": [
    "# Step 1: Fit SuSiE model\n",
    "import rpy2\n",
    "import rpy2.robjects.numpy2ri as numpy2ri\n",
    "import rpy2.robjects as ro\n",
    "from rpy2.rinterface_lib.embedded import RRuntimeError\n",
    "from rpy2.robjects.packages import importr\n",
    "%load_ext rpy2.ipython\n",
    "\n",
    "# Import and run susie\n",
    "susieR = importr('susieR')\n",
    "R_null = ro.rinterface.NULL\n",
    "numpy2ri.activate()\n",
    "susie_obj = susieR.susie(\n",
    "    X=X, y=y, L=10, coverage=0.9\n",
    ")\n",
    "# Extract output\n",
    "alphas = susie_obj.rx2('alpha')\n",
    "susie_sets = susie_obj.rx2('sets')[0]\n",
    "try:\n",
    "    susie_sets = [\n",
    "        np.array(s)-1 for s in susie_sets\n",
    "    ]\n",
    "except TypeError:\n",
    "    susie_sets = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Creating cand groups and running BLiP took 0.34 seconds.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Step 2: create candidate groups based off susie outputs\n",
    "t0 = time.time()\n",
    "cand_groups = pyblip.create_groups.susie_groups(\n",
    "    alphas=alphas,\n",
    "    X=X,\n",
    "    q=0.1, # FDR level\n",
    ")\n",
    "# Step 3: run BLiP\n",
    "detections = pyblip.blip.BLiP(\n",
    "    cand_groups=cand_groups,\n",
    "    error='fdr',\n",
    "    q=0.1,\n",
    "    verbose=False,\n",
    ")\n",
    "elapsed = np.around(time.time() - t0, 2)\n",
    "print(f\"\\nCreating cand groups and running BLiP took {elapsed} seconds.\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the detections from SuSiE and SuSiE + BLiP. As we can see from the smaller group size, SuSiE + BLiP localizes signals more precisely than SuSiE alone. (All detections are true detections in this case.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{68}, {306}, {426}, {184}, {272}, {54}, {382, 383, 384}]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[set(x) for x in susie_sets]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{54}, {68}, {184}, {272}, {306}, {383}, {426}]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x.group for x in detections]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the number of signals increases, SuSiE + BLiP tends to have substantially higher power than SuSiE alone, as discussed in [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Probit spike-and-slab model + BLiP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can run BLiP on top of nearly any regression model, including various models for binary responses. For example, suppose we only observe a binary indicator $Y^{\\star}$ as an outcome. We can apply BLiP directly on top of a sparse probit model in this setting, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: fit probit model\n",
    "ystar = y > 0\n",
    "pm = pyblip.probit.ProbitSpikeSlab(X=X, y=ystar)\n",
    "pm.sample(N=1000, chains=5, bsize=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "BLiP ran in 0.58 seconds.\n",
      "Long-step dual simplex will be used\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Step 2: apply BLiP to posterior samples\n",
    "t0 = time.time()\n",
    "detections = pyblip.blip.BLiP(\n",
    "    samples=pm.betas,\n",
    "    q=0.1,\n",
    "    error='fdr',\n",
    "    verbose=False,\n",
    ")\n",
    "print(f\"\\nBLiP ran in {np.around(time.time() - t0, 2)} seconds.\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we can check that BLiP makes (mostly) correct detections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The true signal variables are [ 54  68 148 184 272 306 383 409 426 471].\n",
      "BLiP correctly detected a signal variable in {68}.\n",
      "BLiP correctly detected a signal variable in {424, 426}.\n",
      "BLiP correctly detected a signal variable in {177, 180, 181, 184, 185}.\n",
      "BLiP correctly detected a signal variable in {263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274}.\n",
      "BLiP correctly detected a signal variable in {313, 306, 308}.\n",
      "BLiP incorrectly detected a signal variable in {58, 53}.\n",
      "BLiP correctly detected a signal variable in {59, 54}.\n",
      "BLiP correctly detected a signal variable in {398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422}.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The true signal variables are {signal_variables}.\")\n",
    "for x in detections:\n",
    "    true_detection = len(x.group.intersection(set(signal_variables))) > 0\n",
    "    if true_detection:\n",
    "        print(f\"BLiP correctly detected a signal variable in {x.group}.\")\n",
    "    else:\n",
    "        print(f\"BLiP incorrectly detected a signal variable in {x.group}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Hierarchical priors to ensure error control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BLiP can wrap on top of nearly any Bayesian model, and in practice, it is fairly robust to some degree of model misspecification (see [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208) for simulations and a discussion of this issue). That said, if the underlying model is extremely poorly specified, BLiP will violate FDR control. For example, in the following problem, the prior indicates that $50\\%$ of the variables are signal variables, whereas in truth only $4\\%$ of the variables are signal variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Sample from an obviously bad spike and slab model\n",
    "lm_bad = pyblip.linear.LinearSpikeSlab(X=X, y=y, p0=0.5, update_p0=False)\n",
    "lm_bad.sample(N=2000, chains=5, burn=200, bsize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BLiP problem has 2263 groups in contention, with 500 active features/locations\n"
     ]
    }
   ],
   "source": [
    "# run blip: FDR control fails because the model is very badly mispecified\n",
    "detections = pyblip.blip.BLiP(\n",
    "    samples=lm_bad.betas,\n",
    "    error='fdr',\n",
    "    q=0.1,\n",
    "    max_pep=0.25,\n",
    "    verbose=True\n",
    ")\n",
    "sigvars = set(signal_variables)\n",
    "fdp = np.mean(\n",
    "    [len(x.group.intersection(sigvars)) == 0 for x in detections]\n",
    ")\n",
    "print(f\"The false positive rate is {np.around(100*fdp)}% due to the mispecified model!\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid this situation, we recommend using **hierarchical priors** on unknown nuisance parameters like the sparsity level in regression problems, with a conservative choice of hyperparameters. The samplers in ``pyblip`` automatically use relatively uninformative hierarchical priors which empirically control the FDR well in a variety of settings. For example, in the previous examples, the prior was quite uninformative, and BLiP still performed quite well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When using MCMC algorithms, we also recommend **running multiple MCMC chains** with different initializations to protect against convergence issues. As discussed in [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208), even when each individual MCMC chain fails to converge, often using multiple chains will overstate the uncertainty in the location of signals, leading to conservative but valid inference.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Changepoint detection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given time series data $(Y_1, \\dots, Y_T)$, suppose we are interested in looking for \"change-points\", or times where the stochastic process changes. Often, we can tell that a process has changed, but we cannot discern exactly when it has changed because each observation $\\{Y_t\\}$ is noisy. The following synthetic dataset gives one example of this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Changepoint series with 5 data-points\n",
    "np.random.seed(123)\n",
    "T = 200\n",
    "_, Y, beta = pyblip.utilities.generate_changepoint_data(\n",
    "    T=T, sparsity=0.04, coeff_size=5,\n",
    ")\n",
    "mu = np.cumsum(beta) # true mean of Y\n",
    "plt.scatter(np.arange(T), Y, color='blue', label='Y')\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Value\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To detect regions where the true mean of $Y$ has changed, we can call the function ``detect changepoints`` which will fit a spike-and-slab changepoint model and apply BLiP on top of it. This only takes one line!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BLiP ran in 11.71.\n",
      "Long-step dual simplex will be used\n"
     ]
    }
   ],
   "source": [
    "detections = pyblip.changepoint.detect_changepoints(\n",
    "    Y=Y, \n",
    "    q=0.1, \n",
    "    sample_kwargs=dict(N=2000, chains=5, bsize=5), # kwargs for the sampler\n",
    "    blip_kwargs=dict(max_pep=0.5, verbose=False) # kwargs for BLiP\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we plot these change-points on top of the raw data and the ground truth. Each output from BLiP is a region which contains a change point with high confidence. The detected regions are shaded in the plot: true detections are in green, and false detections are in orange."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot data-points and ground truth\n",
    "plt.plot(np.arange(T), mu, color='red', label='E[Y]')\n",
    "plt.scatter(np.arange(T), Y, color='blue', label='Y')\n",
    "\n",
    "# Add BLiP detections\n",
    "changepoints = set(np.where(beta != 0)[0].tolist())\n",
    "color_counts = dict(orange=0, green=0) # for legend\n",
    "for j, cs in enumerate(detections):\n",
    "    cs = cs.group\n",
    "    if len(changepoints.intersection(cs)) > 0:\n",
    "        color = 'green'\n",
    "        cstring = 'true positive'\n",
    "    else:\n",
    "        color = 'orange'\n",
    "        cstring = 'false positive'\n",
    "    # Decide whether to add a label\n",
    "    if color_counts[color] == 0:\n",
    "        color_counts[color] += 1\n",
    "        label = f'BLiP detection ({cstring})'\n",
    "    else:\n",
    "        label = None\n",
    "        \n",
    "        \n",
    "    plt.axvspan(\n",
    "        min(cs), max(cs), alpha=min(1, 2 / len(cs)),\n",
    "        color=color,\n",
    "        label=label\n",
    "    )\n",
    "\n",
    "    \n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Value\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, in this example, BLiP does a pretty good job both detecting change-points and quantifying our uncertainty in their locations. The vertical, thin green bars are change-points which have been perfectly localized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Point-source detection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we observe photon counts from a telescope, and we are interested in detecting point-sources (e.g., stars) from the image. Since most images have some blur, we may not be able to perfectly localize each point-source, but BLiP can still help localize them as precisely as possible. Below, we give an example of how to apply BLiP on top of outputs from a pretrained [StarNet model](https://github.com/Runjing-Liu120/DeblendingStarfields). Note that the StarNet model is described in detail in [Liu et. al (2021)](https://arxiv.org/pdf/2102.02409.pdf). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start, we load the simulated $20x20$ image data, which was generated using code from [Liu et. al (2021)](https://arxiv.org/pdf/2102.02409.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load simulated image data\n",
    "npixels = 20\n",
    "image = np.loadtxt(\"data/sim_image.txt\").reshape(2, npixels, npixels)\n",
    "true_locs = np.loadtxt(\"data/sim_locs.txt\").reshape(6, 2)\n",
    "\n",
    "# plot one of the two bands\n",
    "def plot_starnet_sim():\n",
    "    fig, ax = plt.subplots(figsize=(6,4))\n",
    "    sns.heatmap(\n",
    "        np.log(image[1]), \n",
    "        cmap='Greys', ax=ax, \n",
    "        cbar_kws=dict(label='log(Intensity)')\n",
    "    )\n",
    "    # Plot true locations\n",
    "    ax.scatter(\n",
    "        npixels*true_locs[:,1], \n",
    "        npixels*true_locs[:,0], \n",
    "        color='red', \n",
    "        marker='x', \n",
    "        label='True Sources'\n",
    "    )\n",
    "    return fig, ax\n",
    "\n",
    "fig, ax = plot_starnet_sim()\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we load the posterior samples from the pretrained StarNet model. See [here](https://github.com/Runjing-Liu120/DeblendingStarfields) or [here](https://github.com/amspector100/DeblendingStarfields]) for examples of how to fit pretrained StarNet models.\n",
    "\n",
    "Note that the posterior samples are an $(N, n_{\\mathrm{source}}, d)$-shaped array, where $N$ is the number of posterior samples and $d=2$ is the dimension of the image. If ``post_samples[i, j] = (x, y)``, this means that the $i$th posterior sample has asserted that there is a point-source at location $(x,y)$. Since there may be different numbers of point-sources per iteration, NaNs are ignored. See API reference for more details on the data input format.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.07279399, 0.34460315],\n",
       "       [0.05383444, 0.83722878],\n",
       "       [0.12657177, 0.60644835],\n",
       "       [0.54421228, 0.45192835],\n",
       "       [0.76564646, 0.75837231],\n",
       "       [0.87883556, 0.64780414],\n",
       "       [       nan,        nan]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load posterior samples from StarNet\n",
    "post_samples = np.loadtxt('data/post_samples.txt').reshape(996, 7, 2)\n",
    "# Print the location of sources according to the first posterior sample.\n",
    "# The NaN means there are only six estimated sources.\n",
    "post_samples[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.07735128, 0.33859724],\n",
       "       [0.04566601, 0.82996595],\n",
       "       [0.19049473, 0.56281787],\n",
       "       [0.59320527, 0.43181294],\n",
       "       [0.87796324, 0.6558165 ],\n",
       "       [       nan,        nan],\n",
       "       [       nan,        nan]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In contrast, in the 8th iteration, there were five estimated sources.\n",
    "post_samples[8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given these posterior samples, applying BLiP is as easy as calling the ``BLiP_cts`` function. Note that ``BLiP_cts`` is useful in problems where the set of possible signal locations is continuous, for example in this problem, where a point-source could take any location in $[0,20]^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the grid sizes determine the resolutions at which BLiP is applied\n",
    "grid_sizes = np.unique(np.around(np.logspace(np.log10(50), np.log10(4), 25)))\n",
    "detections = pyblip.blip.BLiP_cts(\n",
    "    post_samples,\n",
    "    error='fdr',\n",
    "    q=0.1, \n",
    "    verbose=False,\n",
    "    rescale=False,\n",
    "    grid_sizes=grid_sizes\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot these detections on top of the image to see the detections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.patches as patches\n",
    "\n",
    "fig, ax = plot_starnet_sim()\n",
    "for j, x in enumerate(detections):\n",
    "    center = npixels * x.data['center']\n",
    "     # since rescale=False all radii are the same\n",
    "    radius = npixels* x.data['radii'][0]\n",
    "    if j == 0:\n",
    "        label = 'BLiP detection'\n",
    "    else:\n",
    "        label = None\n",
    "    circle = patches.Circle(\n",
    "        (center[1], center[0]),\n",
    "        radius, \n",
    "        edgecolor=(30/256,144/256,255/256,1),\n",
    "        facecolor=(1,1,1,0), # make interior transparent\n",
    "        linewidth=2,\n",
    "        label=label\n",
    "    )\n",
    "    ax.add_patch(circle)\n",
    "    \n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, BLiP makes four true detections at various resolutions based on the posterior samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Inputs for arbitrary problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, we have reviewed three major problem settings: variable selection, change-point detection, and point-source detection. However, in principle, BLiP can apply to any problem where one is interested in jointly detecting and localizing signals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In generic problems, there are main types of inputs ``BLiP`` can take."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 Posterior samples for discrete problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``pyblip.blip.BLiP`` can take an $(N,p)$-shaped matrix where nonzero values denote the presence of a signal variable. Here, $N$ is the number of posterior samples and $p$ is the number of locations at which a signal can exist. So if ``samples[i,j] != 0``, this indicates that for in the $i$th posterior sample, the $j$th location contains a signal. We call these problems \"discrete\" because $p$ is finite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Posterior samples for continuous problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In some problems, we may be searching for signals in $\\mathbb{R}^d$. In this case, since there are an infinite number of possible locations for signals, we cannot automatically apply ``pyblip.blip.BLiP``.\n",
    "\n",
    "In this setting, ``pyblip.blip.BLiP_cts`` can posterior samples in a different format as an input. In particular, ``pyblip.blip.BLiP_cts`` assumes the posterior samples are an $(N, n_{\\mathrm{source}}, d)$-shaped array, where:\n",
    "1. $N$ is the number of posterior samples \n",
    "2. $d$ is the dimension of the data\n",
    "3. If ``samples[i, j] = (x1, ..., xd)``, this means that the $i$th posterior sample has asserted that there is a point-source at location $(x_1, \\dots, x_d)$. Since there may be different numbers of point-sources per iteration, NaNs are ignored.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 Advanced usage: directly specifying candidate groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A ``CandidateGroup`` object represents a subset of the locations which could potentially contain a signal. For example, in variable selection problems, each ``CandidateGroup`` represents a subset of the covariates. Alternatively, in the following example, each ``CandidateGroup`` represents three circular regions of the globe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyblip.create_groups import CandidateGroup\n",
    "cand_groups = [\n",
    "    CandidateGroup(\n",
    "        group=set([1,2,]), \n",
    "        pep=0.01, \n",
    "        data=dict(\n",
    "            latitude=41.0,\n",
    "            longitude=74.0,\n",
    "            radius=1,\n",
    "            name='big_region',\n",
    "        )\n",
    "    ),\n",
    "    CandidateGroup(\n",
    "        group=set([1,]), \n",
    "        pep=0.3, \n",
    "        data=dict(\n",
    "            latitude=41.5,\n",
    "            longitude=74.0,\n",
    "            radius=0.01,\n",
    "            name='sub_region1',\n",
    "        )\n",
    "    ),\n",
    "    CandidateGroup(\n",
    "        group=set([2,]), \n",
    "        pep=0.2, \n",
    "        data=dict(\n",
    "            latitude=40.5,\n",
    "            longitude=74.0,\n",
    "            radius=0.01,\n",
    "            name='sub_region2',\n",
    "        )\n",
    "    ),\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each ``CandidateGroup`` has three attributes. \n",
    "\n",
    "1. The ``pep`` attribute specifies the posterior error probability, or the posterior probability that the candidate group does *not* contain a signal.\n",
    "\n",
    "\n",
    "2. The ``group`` attribute is a set of positive integers such that two candidate groups overlap if and only if their ``group`` attributes overlap. For example, above, the group attributes suggest that the ``big_region`` overlaps with ``sub_region1`` and ``sub_region2``, but ``sub_region1`` and ``sub_region2`` do not overlap.\n",
    "\n",
    "\n",
    "3. The ``data`` attribute is a optional dictionary that contains miscallaneous metadata. BLiP largely ignores the ``data`` attribute."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can directly apply BLiP on top of a list of candidate groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "BLiP detected the candidate groups named: ['big_region']\n",
      "Long-step dual simplex will be used\n"
     ]
    }
   ],
   "source": [
    "detections = pyblip.blip.BLiP(\n",
    "    cand_groups=cand_groups,\n",
    "    verbose=False,\n",
    "    q=0.1,\n",
    "    error='fdr',\n",
    ")\n",
    "print(f\"\\nBLiP detected the candidate groups named: {[x.data['name'] for x in detections]}\")"
   ]
  }
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