### Install Pomegranate from GitHub

Source: https://pomegranate.readthedocs.io/en/latest/_sources/install.rst

Installs the bleeding-edge version of pomegranate directly from its GitHub repository. This involves cloning the repository and running the setup script.

```bash
git clone https://github.com/jmschrei/pomegranate
cd pomegranate
python setup.py install
```

--------------------------------

### Environment Setup and Version Check (Python, PyTorch)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/C_Feature_Tutorial_3_Out_Of_Core_Learning

This snippet sets up the Python environment for out-of-core learning examples. It imports necessary libraries like torch and pomegranate, sets random seeds for reproducibility, and displays version information for torch and pomegranate, along with system details.

```python
%pylab inline
import torch

numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p torch,pomegranate

```

--------------------------------

### Setup and Environment Information

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_2_General_Mixture_Models.ipynb

Imports necessary libraries (numpy, matplotlib, seaborn, torch) and loads the pomegranate library. It also displays environment and package versions using %watermark. This setup is crucial for running the subsequent examples.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')

import torch

from pomegranate.gmm import GeneralMixtureModel
from pomegranate.distributions import *


numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p numpy,scipy,torch,pomegranate
```

--------------------------------

### Import Libraries and Setup Environment

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_5_Markov_Chains

Imports necessary libraries like torch and pomegranate, and sets up the environment for displaying plots and version information. This is a standard setup for running examples.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')
import torch

%load_ext watermark
%watermark -m -n -p torch,pomegranate

```

--------------------------------

### Install Pomegranate using Pip

Source: https://pomegranate.readthedocs.io/en/latest/_sources/install.rst

Installs the pomegranate Python package and its dependencies using pip. This is the recommended and simplest installation method.

```bash
pip install pomegranate
```

--------------------------------

### Initialize Pomegranate and Watermark

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/C_Feature_Tutorial_3_Out_Of_Core_Learning.ipynb

Initializes the Pomegranate environment and displays version information for PyTorch and Pomegranate. This setup is crucial for reproducible results and understanding the software environment.

```python
%pylab inline
import torch

numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p torch,pomegranate
```

--------------------------------

### Setup Environment and Load Watermark

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_6_Bayesian_Networks.ipynb

This code snippet sets up the Python environment by importing necessary libraries like numpy and matplotlib, and then loads the watermark extension to display package versions.

```python
from pomegranate.distributions import Categorical
from pomegranate.distributions import ConditionalCategorical
from pomegranate.bayesian_network import BayesianNetwork

d1 = Categorical([[0.1, 0.9]])
d2 = ConditionalCategorical([[[0.4, 0.6], [0.3, 0.7]]])

model = BayesianNetwork([d1, d2], [(d1, d2)])
```

--------------------------------

### Calculate Probability of Data Examples (Python)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_7_Factor_Graphs

Calculates the probability of each data example in X given the fitted FactorGraph model. The probability is factorized across factors and marginal distributions.

```python
print(model.probability(X[:1]))
```

--------------------------------

### Import Libraries and Setup for HMMs

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models

This snippet imports necessary libraries such as seaborn, torch, and numpy, and sets up the environment for numerical operations and plotting. It also loads the watermark extension to display package versions and system information.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')

import torch

numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p numpy,scipy,torch,pomegranate

```

--------------------------------

### Set up environment and display package versions

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models.ipynb

This code snippet sets up the environment for analysis by importing necessary libraries like numpy and matplotlib, and then uses the %watermark magic command to display the versions of installed packages including numpy, scipy, torch, and pomegranate. It also configures numpy for better output formatting and sets a random seed for reproducibility.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')

import torch

numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p numpy,scipy,torch,pomegranate
```

--------------------------------

### KMeans Model Fitting Timing - Python

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/C_Feature_Tutorial_1_GPU_Usage

Compares the time required to fit a KMeans model on CPU versus GPU. This example initializes two KMeans models, one for CPU and one for GPU, and times their respective fit methods using a large dataset.

```python
from pomegranate.kmeans import KMeans

model1 = KMeans(512)
model2 = KMeans(512)

%timeit -n 1 -r 1 model1.fit(X)
%timeit -n 1 -r 1 model2.cuda().fit(X.cuda())
```

--------------------------------

### Accessing Model Probabilities (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_5_Markov_Chains.ipynb

Provides examples of accessing the probability distributions within a Markov chain model. This allows inspection of the learned transition probabilities between states. The output shows the probability tensors for different distributions within the model.

```python
model.distributions[0].probs
```

```python
model.distributions[1].probs[0]
```

```python
model.distributions[2].probs[0]
```

--------------------------------

### Batched Training for Normal Distribution (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/C_Feature_Tutorial_3_Out_Of_Core_Learning.ipynb

This example illustrates batched training for a Normal distribution using Pomegranate's out-of-core API. It iterates through data batches, summarizes each batch, and then reconstructs the distribution from the accumulated summaries, suitable for large datasets.

```python
dist = Normal()

for i in range(10):
    X_batch = torch.randn(1000, 20) # Mimics loading a batch of data
    dist.summarize(X_batch)
    del X_batch # Discard the batch after summarization
    
dist.from_summaries()
```

--------------------------------

### Calculate Log Probability of Data Examples (Python)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_7_Factor_Graphs

Computes the log probability for each data example in X using the FactorGraph model. This is often preferred for numerical stability compared to direct probability calculations.

```python
print(model.log_probability(X))
```

--------------------------------

### Makefile for Development (Makefile)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/whats_new.rst

A top-level Makefile is provided for development convenience, supporting two conda environments (py2.7 and py3.6 by default). It includes targets for installation, testing, cleaning, and notebook testing, with options to override environment names and control error handling during notebook tests.

```makefile
# Example usage:
# make PY3_ENV=py3.6.2 biginstall
# make ALLOW_ERRORS=--allow-errors nbtest

install:
	t# Installation commands
test:
	# Testing commands
bigclean:
	# Clean build commands
nbtest:
	# Jupyter notebook testing commands
```

--------------------------------

### Initialize and Fit Bayesian Network with Known Structure

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_6_Bayesian_Networks.ipynb

Initializes a Bayesian network with a predefined structure and then fits it to the data `X`. This is useful when the network's architecture is known beforehand, and only the parameters need to be learned. The example demonstrates learning the parameters for a network with a single dependency.

```python
model3 = BayesianNetwork(structure=[(), (0,)])
model3.fit(X)

model3.distributions[1].probs[0]
```

--------------------------------

### Initialize DenseHMM with Explicit Parameters

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models

Creates a DenseHMM by explicitly providing a list of distributions, a dense transition matrix, and optional start and end probabilities. This method is suitable for defining a known HMM structure.

```python
from pomegranate.hmm import DenseHMM
from pomegranate.distributions import Normal
import torch
import matplotlib.pyplot as plt

# Assuming d1 and d2 are pre-defined distributions, and X is pre-defined data
# Example placeholder distributions and data:
d1 = Normal(0, 1)
d2 = Normal(1, 1)
X = torch.randn(100, 10) # Example data

model = DenseHMM([d1, d2], edges=[[0.89, 0.1], [0.1, 0.9]], starts=[0.5, 0.5], ends=[0.01, 0.0])

plt.plot(model.predict_proba(X)[0], label=['background', 'CG island'])
plt.legend()
plt.show()
```

--------------------------------

### Initialize DenseHMM with Priors in Pomegranate

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/C_Feature_Tutorial_4_Priors_and_Semi-supervised_Learning

This code snippet demonstrates how to initialize a DenseHMM model in Pomegranate. It defines two Normal distributions and sets up the transition matrix and starting probabilities for the HMM. The priors are also specified as a 3D tensor.

```python
from pomegranate.hmm import DenseHMM
from pomegranate.distributions import Normal

d1 = Normal([1.0], [1.0], covariance_type='diag')
d2 = Normal([3.0], [1.0], covariance_type='diag')

model = DenseHMM([d1, d2], [[0.7, 0.3], [0.3, 0.7]], starts=[0.4, 0.6])

```

--------------------------------

### Import Libraries and Setup for Bayes Classifier

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_3_Bayes_Classifier

This snippet imports necessary libraries like torch, seaborn, and components from pomegranate for building and visualizing probabilistic models. It also sets up the environment for displaying plots and watermarking the session with package versions.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')

import torch

from pomegranate.bayes_classifier import BayesClassifier
from pomegranate.distributions import *


numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p numpy,scipy,torch,pomegranate

```

--------------------------------

### Import Libraries and Setup for Mixture Models

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_2_General_Mixture_Models

This code block imports necessary libraries such as torch, seaborn, and components from pomegranate for implementing mixture models. It also sets up random seeds and display options for reproducibility and clear output. The watermark extension is used to display environment and package versions.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')

import torch

from pomegranate.gmm import GeneralMixtureModel
from pomegranate.distributions import *


numpy.random.seed(0)
numpy.set_printoptions(suppress=True)

%load_ext watermark
%watermark -m -n -p numpy,scipy,torch,pomegranate


```

--------------------------------

### Fit DenseHMM with Default Iterations

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models

Demonstrates fitting a DenseHMM model with default iteration settings. It initializes categorical distributions, transition edges, start and end probabilities, and then fits the model to data `X`. The output shows the iterative improvement in the model's likelihood.

```python
d1 = Categorical([[0.25, 0.25, 0.25, 0.25]])
d2 = Categorical([[0.10, 0.40, 0.40, 0.10]])

edges = [[0.89, 0.1], [0.1, 0.9]]
starts = [0.5, 0.5]
ends = [0.01, 0.0]

model = DenseHMM([d1, d2], edges=edges, starts=starts, ends=ends, verbose=True)
model.fit(X)
```

--------------------------------

### Initialize and Fit Model with Data (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/faq.rst

Demonstrates how to initialize a model with hyperparameters and then fit it to data using the `fit` function, following the scikit-learn API. Some models may allow blank initialization, while others require specific parameters like distributions for mixture models or order for Markov chains.

```python
from pomegranate import NormalDistribution

# Example: Initialize a model and fit it to data
model = NormalDistribution().fit(X)
```

--------------------------------

### log_probability() Method

Source: https://pomegranate.readthedocs.io/en/latest/api

Calculates the log probability of each example given the distribution's parameters. Assumes examples are in a 2D format.

```APIDOC
## Method: log_probability(_X_)

### Description
Calculate the log probability of each example. This method calculates the log probability of each example given the parameters of the distribution. The examples must be given in a 2D format. For a Bernoulli distribution, each entry in the data must be either 0 or 1.

Note: This differs from some other log probability calculation functions, like those in torch.distributions, because it is not returning the log probability of each feature independently, but rather the total log probability of the entire example.

### Method
(Implicitly called by fit, no direct HTTP method)

### Endpoint
(N/A)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
* **X** (list, tuple, numpy.ndarray, torch.Tensor) - Required - A set of examples to evaluate. Shape should be (-1, self.d).

### Request Example
```json
{
  "X": [[0.1, 0.2], [0.3, 0.4]]
}
```

### Response
#### Success Response (200)
* **logp** (torch.Tensor) - The log probability of each example. Shape is (-1,).

#### Response Example
```json
{
  "logp": [-1.23, -0.45]
}
```
```

--------------------------------

### Initialize a Markov Chain Model

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_5_Markov_Chains

Demonstrates how to initialize a MarkovChain model. You can either pass pre-fit distributions or specify the 'k' parameter to let pomegranate automatically construct the necessary distributions.

```python
from pomegranate.markov_chain import MarkovChain

model = MarkovChain(k=3)

```

--------------------------------

### log_probability(_X_)

Source: https://pomegranate.readthedocs.io/en/latest/api

Calculate the log probability of each example given the parameters of the distribution. The examples must be given in a 2D format.

```APIDOC
## POST /log_probability

### Description
Calculate the log probability of each example given the parameters of the distribution. The examples must be given in a 2D format. For a gamma distribution, the data must be non-negative.
Note: This differs from some other log probability calculation functions, like those in torch.distributions, because it is not returning the log probability of each feature independently, but rather the total log probability of the entire example.

### Method
POST

### Endpoint
/log_probability

### Parameters
#### Request Body
- **X** (list, tuple, numpy.ndarray, torch.Tensor) - Required - A set of examples to evaluate. Shape: (-1, self.d)

### Request Example
```json
{
  "X": "[[1.0, 2.0], [3.0, 4.0]]"
}
```

### Response
#### Success Response (200)
- **logp** (torch.Tensor) - The log probability of each example. Shape: (-1,)

#### Response Example
```json
{
  "logp": "[-1.23, -4.56]"
}
```
```

--------------------------------

### Categorical.log_probability()

Source: https://pomegranate.readthedocs.io/en/latest/api

Calculates the log probability of each example. The examples must be given in a 2D format. For a categorical distribution, each entry in the data must be an integer in the range [0, n_keys).

```APIDOC
## POST /Categorical/log_probability

### Description
Calculate the log probability of each example. The examples must be given in a 2D format. For a categorical distribution, each entry in the data must be an integer in the range [0, n_keys). Note: This differs from some other log probability calculation functions, like those in torch.distributions, because it is not returning the log probability of each feature independently, but rather the total log probability of the entire example.

### Method
POST

### Endpoint
/Categorical/log_probability

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
- **X** (list, tuple, numpy.ndarray, torch.Tensor) - Required - A set of examples to evaluate. Shape should be (-1, self.d).

### Request Example
```json
{
  "X": [[0, 1], [1, 0]]
}
```

### Response
#### Success Response (200)
- **logp** (torch.Tensor) - The log probability of each example. Shape is (-1,).

#### Response Example
```json
{
  "logp": [-0.5, -0.7]
}
```
```

--------------------------------

### Initialize Bayesian Network with Distributions and Edges

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_6_Bayesian_Networks

Demonstrates initializing a Bayesian Network by providing a list of distributions and a list of edges representing dependencies. This method directly defines the network's structure and components.

```python
from pomegranate.distributions import Categorical
from pomegranate.distributions import ConditionalCategorical
from pomegranate.bayesian_network import BayesianNetwork

d1 = Categorical([[0.1, 0.9]])
d2 = ConditionalCategorical([[[0.4, 0.6], [0.3, 0.7]]])

model = BayesianNetwork([d1, d2], [(d1, d2)])

```

--------------------------------

### Calculate Probability of Examples

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_6_Bayesian_Networks.ipynb

Computes the probability of each example in the input data `X` according to the learned Bayesian network model. This leverages the factorization of the joint probability distribution along the graph structure.

```python
model.probability(X)
```

--------------------------------

### Initialize GeneralMixtureModel with Distributions and Priors

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_2_General_Mixture_Models.ipynb

This code demonstrates how to initialize a GeneralMixtureModel with pre-defined probability distributions (Exponential in this case) and their corresponding prior probabilities. This is useful when you have prior knowledge about the distributions and their weights.

```python
d1 = Exponential([1.3, 3.3])
d2 = Exponential([2.2, 0.4])

model = GeneralMixtureModel([d1, d2], priors=[0.2, 0.8])
```

--------------------------------

### Define HMM Transition Probabilities and Start Probabilities (Python)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models

Sets the transition probabilities between hidden states and the initial probabilities for starting in each state. This defines the HMM's structure and how it moves between states based on observations.

```python
model.add_edge(model.start, d1, 0.5)
model.add_edge(model.start, d2, 0.5)
model.add_edge(d1, d1, 0.9)
model.add_edge(d1, d2, 0.1)
model.add_edge(d2, d1, 0.1)
model.add_edge(d2, d2, 0.9)
```

--------------------------------

### Calculate Log Probability for Bernoulli Distribution - Pomegranate

Source: https://pomegranate.readthedocs.io/en/latest/api

Calculates the log probability of each example given the Bernoulli distribution's parameters. Input data `X` must be 2D, with each entry being 0 or 1. This method returns the total log probability for each example, not feature-wise.

```python
import torch
from pomegranate import Bernoulli

probs = [0.7, 0.3]
bernoulli_dist = Bernoulli(probs=probs)

X = torch.tensor([[1, 0], [0, 1], [1, 1]])
log_probs = bernoulli_dist.log_probability(X)
print(log_probs)

```

--------------------------------

### Out-of-Core Learning with Summarize and FromSummaries (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/faq.rst

Illustrates the process of out-of-core learning in pomegranate. This involves using the `summarize` method on data chunks to obtain sufficient statistics, which are then added and used to update model parameters via `from_summaries`.

```python
from pomegranate import NormalDistribution

# Assume model is initialized
model = NormalDistribution()

# Process chunks of data
summaries = []
for chunk in data_chunks:
    summaries.append(model.summarize(chunk))

# Add summaries and update model parameters
combined_summaries = add_summaries(summaries) # Function to add summaries
model.from_summaries(combined_summaries)
```

--------------------------------

### Sample from Markov Models (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_5_Markov_Chains.ipynb

Illustrates how to generate samples from a trained Markov chain model. This is useful for simulating future sequences or understanding the model's generative capabilities. The sampling process can produce a large number of samples for analysis. Dependencies include PyTorch.

```python
X_sample = model.sample(100000).type(torch.float32)
```

--------------------------------

### Calculate Log Probability (Pomegranate Normal)

Source: https://pomegranate.readthedocs.io/en/latest/api

Computes the log probability of each example given the Normal distribution's parameters. Requires input data in a 2D format.

```python
import numpy as np
from pomegranate.distributions import Normal

dist = Normal(means=[0], covs=[[1]])
X = np.array([[1.0], [-1.0]])
log_probs = dist.log_probability(X)
print(log_probs)

```

--------------------------------

### Initialize Bayesian Network Programmatically

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_6_Bayesian_Networks

Shows an alternative way to create a Bayesian Network by first initializing an empty network and then adding distributions and edges using dedicated methods. This offers more flexibility in building the network step-by-step.

```python
from pomegranate.distributions import Categorical
from pomegranate.distributions import ConditionalCategorical
from pomegranate.bayesian_network import BayesianNetwork

d1 = Categorical([[0.1, 0.9]])
d2 = ConditionalCategorical([[[0.4, 0.6], [0.3, 0.7]]])

model2 = BayesianNetwork()
model2.add_distributions([d1, d2])
model2.add_edge(d1, d2)

```

--------------------------------

### Generate Random Data (Python, PyTorch)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/C_Feature_Tutorial_3_Out_Of_Core_Learning

Generates a tensor of random numbers using PyTorch for use in out-of-core learning examples. The data is a 1000x5 tensor, suitable for training a multivariate distribution.

```python
X = torch.randn(1000, 5)

```

--------------------------------

### Initialize Bayesian Network Programmatically

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_6_Bayesian_Networks.ipynb

Demonstrates an alternative method to create a Bayesian Network by first adding distributions and then defining edges between them using `add_distributions` and `add_edge` methods.

```python
model2 = BayesianNetwork()
model2.add_distributions([d1, d2])
model2.add_edge(d1, d2)
```

--------------------------------

### Rebuildconda Script for Conda Environments (Shell)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/whats_new.rst

A convenience script `rebuildconda` is available for development to remove and recreate conda environments. It defaults to rebuilding the 'py2.7' environment but can be configured for other environments. This is useful for testing different environment setups.

```bash
# Example usage:
# ./rebuildconda 2.7.9 ; make PY2_ENV=py2.7.9 bigclean py2build py2test py2install nbtest ; source deactivate ; conda env remove --name py2.7.9

# Default rebuilds 'py2.7' environment
./rebuildconda
```

--------------------------------

### Summarize Data for Normal Distribution (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/C_Feature_Tutorial_3_Out_Of_Core_Learning.ipynb

This code snippet demonstrates how to initialize a Normal distribution, summarize data (X) from it, and then reconstruct the distribution parameters from these summaries. It's useful for understanding the internal state of the distribution after processing data.

```python
dist = Normal()
dist.summarize(X)
dist.from_summaries()
dist.means, dist.covs
```

--------------------------------

### Predict Most Likely Value - Python

Source: https://pomegranate.readthedocs.io/en/latest/_sources/api.rst

Returns the most likely inferred value for each example in the data. For Bayesian networks with incomplete data, it infers the most likely variable values. For other models, it identifies the most likely component explaining the data.

```python
>>> model.predict(X)
```

--------------------------------

### Add return_history to fit/from_samples (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/whats_new.rst

Introduces the `return_history` parameter to the `fit` and `from_samples` methods in various Pomegranate models. This parameter allows the methods to return the history callback along with the fitted model, enhancing the tracking of model fitting progress.

```python
model.fit(X, return_history=True)
model.from_samples(X, return_history=True)
```

--------------------------------

### Calculate Log Probability of Data - Python

Source: https://pomegranate.readthedocs.io/en/latest/_sources/api.rst

Calculates the log probability of a given set of examples using a trained model. This method is numerically more stable than `probability` and is used internally for its calculation. It accepts 2D or 3D data.

```python
>>> model.log_probability(X)
```

--------------------------------

### Calculate Probability of Data - Python

Source: https://pomegranate.readthedocs.io/en/latest/_sources/api.rst

Calculates the probability of a given set of examples using a trained model. This method takes 2D or 3D data and returns a vector of probabilities. It is derived from log probabilities for numerical stability.

```python
>>> model.probability(X)
```

--------------------------------

### Initialize and Fit Naive Bayes Classifier

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_3_Bayes_Classifier.ipynb

Demonstrates how to initialize and fit a Naive Bayes classifier in Pomegranate. It shows two methods: providing pre-learned distributions or providing uninitialized distributions that will be fitted to the data.

```python
# Initialize with learned distributions
clf = BayesClassifier.from_samples(Normal, X, y)

# Initialize with uninitialized distributions
clf = BayesClassifier(n_components=2)
clf.fit(X, y, n_iter=10, tol=0.01)
```

--------------------------------

### Format Date in JavaScript

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_2_General_Mixture_Models.ipynb

Formats a Date object into a human-readable string. This example shows a basic format, but can be extended to include various date and time components. It utilizes the built-in `Date` object methods.

```javascript
function formatDate(date) {
  const options = { year: 'numeric', month: 'long', day: 'numeric' };
  return date.toLocaleDateString(undefined, options);
}
```

--------------------------------

### Summarize and Reconstruct Markov Chain

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_5_Markov_Chains

Explains how to use the 'summarize' and 'from_summaries' methods for Markov chains. This requires data to be three-dimensional and of consistent length within each summarization call.

```python
X = torch.randint(2, size=(30, 8, 1))

model.summarize(X[:10])
model.summarize(X[10:])
model.from_summaries()

```

--------------------------------

### Initialize a Simple Factor Graph with Categorical Distributions

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_7_Factor_Graphs.ipynb

This Python code demonstrates the initialization of a basic factor graph using pomegranate. It sets up two marginal categorical distributions and prepares for their integration into a factor graph structure. This is a foundational step for building more complex factor graph models.

```python
from pomegranate.distributions import Categorical
from pomegranate.distributions import JointCategorical
from pomegranate.factor_graph import FactorGraph

m1 = Categorical([[0.5, 0.5]])
m2 = Categorical([[0.5, 0.5]])


```

--------------------------------

### Manual Log Probability Calculation

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_6_Bayesian_Networks.ipynb

Manually calculates the log probability of examples by summing the log probabilities of individual variables based on their parents, as defined by the model's structure and distributions. This serves as a verification method for the `log_probability` method.

```python
model.distributions[0].log_probability(X[:,:1]) + model.distributions[1].log_probability(X[:, :, None])
```

--------------------------------

### Import Libraries and Check Versions

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_5_Markov_Chains.ipynb

Imports necessary libraries like pylab, seaborn, and torch, and loads the watermark extension to display package versions. This is useful for reproducibility and debugging.

```python
%pylab inline
import seaborn; seaborn.set_style('whitegrid')
import torch

%load_ext watermark
%watermark -m -n -p torch,pomegranate
```

--------------------------------

### DenseHMM Initialization Parameters

Source: https://pomegranate.readthedocs.io/en/latest/api

This section details the parameters used for initializing the DenseHMM class. It covers distributions, prior probabilities, maximum iterations, convergence tolerance, inertia for parameter updates, freezing parameters, data checking, and verbosity during training.

```python
class DenseHMM(
    _distributions=None,
    _edges=None,
    _starts=None,
    _ends=None,
    _init='random',
    _max_iter=1000,
    _tol=0.1,
    _sample_length=None,
    _return_sample_paths=False,
    _inertia=0.0,
    _frozen=False,
    _check_data=True,
    _random_state=None,
    _verbose=False
)
```

--------------------------------

### Initialize Pomegranate Distributions with Parameters (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_1_Distributions.ipynb

Demonstrates initializing various pomegranate probability distributions (Normal, Exponential, Categorical) with predefined parameters. It shows that parameters can be provided as lists, tuples, NumPy arrays, or PyTorch tensors, and highlights the 'diag' covariance type for Normal distributions.

```python
d1 = Normal([0.3, 0.7, 1.1], [1.1, 0.3, 1.8], covariance_type='diag')
d2 = Exponential([0.8, 1.4, 4.1])
d3 = Categorical([[0.3, 0.2, 0.5], [0.2, 0.1, 0.7]])

d11 = Normal((0.3, 0.7, 1.1), (1.1, 0.3, 1.8), covariance_type='diag')
d12 = Normal(numpy.array([0.3, 0.7, 1.1]), numpy.array([1.1, 0.3, 1.8]), covariance_type='diag')
d13 = Normal(torch.tensor([0.3, 0.7, 1.1]), torch.tensor([1.1, 0.3, 1.8]), covariance_type='diag')
```

--------------------------------

### Initialize SparseHMM with Edges and Distributions (Python)

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models.ipynb

This snippet demonstrates initializing a SparseHMM model by directly providing distributions and a list of edges. The edges define the transitions between states, including their probabilities. This method is suitable for defining HMMs with known transition structures.

```python
from pomegranate.hmm import SparseHMM

edges = [
    [d1, d1, 0.89],
    [d1, d2, 0.1],
    [d2, d1, 0.1],
    [d2, d2, 0.9]
]

model = SparseHMM([d1, d2], edges=edges, starts=[0.5, 0.5], ends=[0.01, 0.0])

plt.plot(model.predict_proba(X)[0], label=['background', 'CG island'])
plt.legend()
plt.show()
```

--------------------------------

### Initialize DenseHMM Distributions with K-Means

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models

Creates a DenseHMM with uninitialized distributions and then initializes them using k-means clustering when provided with data via the `_initialize` method. Transition edges can be initialized to uniform probabilities if not provided.

```python
from pomegranate.hmm import DenseHMM
from pomegranate.distributions import Normal
import torch

X3 = torch.randn(100, 50, 2)

# Distributions will be initialized using k-means
model3 = DenseHMM([Normal(), Normal(), Normal()], verbose=True)
model3._initialize(X3)

# Accessing the means of the initialized distributions
print(model3.distributions[0].means, model3.distributions[1].means, model3.distributions[2].means)
```

--------------------------------

### Summarize and Update Pomegranate Model Parameters

Source: https://pomegranate.readthedocs.io/en/latest/_sources/tutorials/B_Model_Tutorial_7_Factor_Graphs.ipynb

This example illustrates the summarization API in Pomegranate for training. It shows how to summarize batches of data using `summarize` and then update the model's factor parameters using `from_summaries`. This process only affects factor parameters, not marginal distributions.

```python
model.summarize(X[:3])
model.from_summaries()
```

--------------------------------

### Initialize Mixture Model with Existing Distributions (Python)

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_2_General_Mixture_Models

Initializes a GeneralMixtureModel using pre-defined probability distributions and prior probabilities. This is useful when you have existing distribution objects and their associated prior weights.

```python
from pomegranate import GeneralMixtureModel, Exponential

d1 = Exponential([1.3, 3.3])
d2 = Exponential([2.2, 0.4])

model = GeneralMixtureModel([d1, d2], priors=[0.2, 0.8])
```

--------------------------------

### Recreate Model Parameters from Summaries

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_1_Distributions

Demonstrates the `from_summaries` method for Pomegranate `Normal` distribution objects. It shows how to recreate the model's parameters (means) from the summarized statistics, confirming that batch summarization and full summarization yield the same results.

```python
d.from_summaries()
d2.from_summaries()
d.means, d2.means
```

--------------------------------

### SparseHMM Initialization Parameters

Source: https://pomegranate.readthedocs.io/en/latest/api

Defines the parameters for initializing a SparseHMM model. These include distributions, transition matrix (edges), start and end probabilities, inertia for parameter updates, and flags for freezing parameters and checking data. The `_class_pomegranate.hmm.SparseHMM` constructor accepts these arguments to configure the HMM.

```python
class _pomegranate.hmm.SparseHMM(_distributions=None, _edges=None, _starts=None, _ends=None, _init='random', _max_iter=1000, _tol=0.1, _sample_length=None, _return_sample_paths=False, _inertia=0.0, _frozen=False, _check_data=True, _random_state=None, _verbose=False)
```

--------------------------------

### Predict Probabilities with Mixture Model

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_2_General_Mixture_Models

This snippet shows how to get the probability of each data point belonging to each component in the mixture model using the `predict_proba` method. This returns the responsibility matrix, which are the likelihoods multiplied by priors and normalized. It requires a fitted model and input data `X`.

```python
model.predict_proba(X)[::15]
```

--------------------------------

### Inspect Markov Chain Distributions

Source: https://pomegranate.readthedocs.io/en/latest/tutorials/B_Model_Tutorial_5_Markov_Chains

Illustrates how to inspect the fitted distributions within the MarkovChain model. This allows verification of the learned probabilities for different states and transitions.

```python
print(model.distributions[0].probs[0])
print(model.distributions[1].probs[0])
print(model.distributions[2].probs[0])

```