largekalman 0.2.1

Kalman filtering and smoothing for larger-than-memory datasets

largekalman

Kalman filtering and smoothing for larger-than-memory datasets.

Features

• Memory-efficient: Processes data in batches, writing intermediate results to disk
• RTS Smoother: Full Rauch-Tung-Striebel smoothing with lag-1 covariance
• Sufficient statistics: Returns statistics needed for EM parameter estimation
• Non-square observation matrices: Supports observation dimension different from latent dimension

Installation

pip install largekalman

Requirements: A C compiler (gcc) is needed to build the native extension.

• Ubuntu/Debian: sudo apt install build-essential
• macOS: xcode-select --install
• Fedora: sudo dnf install gcc

Quick Start

import largekalman

# Define state space model parameters
F = [[0.9, 0.1], [0.0, 0.9]]  # Transition matrix
Q = [[0.1, 0.0], [0.0, 0.1]]  # Process noise covariance
H = [[1.0, 0.0], [0.0, 1.0]]  # Observation matrix
R = [[0.5, 0.0], [0.0, 0.5]]  # Observation noise covariance

# Observations as an iterator (can be a generator for large datasets)
observations = [[1.2, 0.8], [1.5, 1.1], [1.8, 1.3], ...]

# Run the smoother
generator, stats = largekalman.smooth(
    'tmp_folder',      # Temporary folder for intermediate files
    F, Q, H, R,
    iter(observations),
    store_observations=False  # Don't keep observations in memory
)

# Iterate over smoothed estimates
for mu, cov, lag1_cov in generator:
    print(f"Smoothed mean: {mu}")
    print(f"Smoothed covariance: {cov}")
    print(f"Lag-1 covariance: {lag1_cov}")

# Sufficient statistics for EM
print(f"Number of datapoints: {stats['num_datapoints']}")
print(f"Sum of latent means: {stats['latents_mu_sum']}")
print(f"Sum of E[x_t x_t^T]: {stats['latents_cov_sum']}")
print(f"Sum of E[x_{t+1} x_t^T]: {stats['latents_cov_lag1_sum']}")

API Reference

smooth(tmp_folder, F, Q, H, R, observations_iter, store_observations=True, batch_size=10000)

Run Kalman filter forward pass followed by RTS smoother backward pass.

Parameters:

• tmp_folder: Path to folder for temporary files (created if doesn't exist)
• F: Transition matrix (n_latents x n_latents)
• Q: Process noise covariance (n_latents x n_latents)
• H: Observation matrix (n_obs x n_latents)
• R: Observation noise covariance (n_obs x n_obs)
• observations_iter: Iterator over observation vectors
• store_observations: If False, delete observations file after processing
• batch_size: Number of timesteps to process at once

Returns:

• generator: Yields (mu, cov, lag1_cov) tuples for each timestep
• stats: Dictionary of sufficient statistics

Sufficient Statistics

The stats dictionary contains:

• num_datapoints: Number of observations processed
• latents_mu_sum: Sum of smoothed means
• latents_cov_sum: Sum of E[x_t x_t^T] (includes outer product of means)
• latents_cov_lag1_sum: Sum of E[x_{t+1} x_t^T] for consecutive pairs
• obs_sum: Sum of observations
• obs_obs_sum: Sum of E[y_t y_t^T]
• obs_latents_sum: Sum of E[y_t x_t^T]

EM Parameter Estimation

Use the built-in em function to learn model parameters from data:

import largekalman

# Fit parameters using EM (H fixed by default for identifiability)
params, history = largekalman.em(
    'tmp_folder',
    observations,
    n_latents=2,
    n_iters=20,
    verbose=True
)

print(f"Fitted F:\n{params['F']}")
print(f"Fitted Q:\n{params['Q']}")
print(f"Fitted R:\n{params['R']}")

# Fix multiple parameters
params, _ = largekalman.em('tmp', obs, n_latents=2, fixed='HR')

em(tmp_folder, observations, n_latents, n_obs=None, n_iters=20, init_params=None, fixed='H', verbose=False)

Fit Kalman filter parameters using Expectation-Maximization.

Parameters:

• tmp_folder: Path to folder for temporary files
• observations: List of observation vectors
• n_latents: Number of latent dimensions
• n_obs: Number of observation dimensions (inferred from data if None)
• n_iters: Number of EM iterations
• init_params: Optional dict with initial parameters {'F', 'Q', 'H', 'R'}
• fixed: String of parameters to hold fixed, e.g. 'H' or 'HR'. Required for identifiability.
• verbose: Print progress if True

Returns:

• params: Dict with fitted parameters {'F', 'Q', 'H', 'R'}
• history: List of parameter dicts from each iteration

em_step(tmp_folder, F, Q, H, R, observations)

Run a single EM iteration for custom control over the optimization.

Returns:

• F_new, Q_new, H_new, R_new: Updated parameters as numpy arrays
• stats: Sufficient statistics from the E-step

License

MIT License