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Grid Search

GridSearch

Base class for performing grid search over Langevin Monte Carlo hyperparameters.

Parameters

gammas : list List of gamma (friction) values to try. etas : list List of eta (step size) values to try. xis : list List of xi values (used only for third-order methods). If None, fourth-order is assumed. N : int Number of MCMC samples to draw for each parameter configuration. Required. seed : int Random seed for reproducibility. show_progress : bool, default=True Whether to show a progress bar during the grid search.

Source code in holmc/utils/gridsearch.py 
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class GridSearch:
    """
    Base class for performing grid search over Langevin Monte Carlo
    hyperparameters.

    Parameters
    ----------
    gammas : list
        List of gamma (friction) values to try.
    etas : list
        List of eta (step size) values to try.
    xis : list
        List of xi values (used only for third-order methods). If None,
        fourth-order is assumed.
    N : int
        Number of MCMC samples to draw for each parameter configuration.
        Required.
    seed : int
        Random seed for reproducibility.
    show_progress : bool, default=True
        Whether to show a progress bar during the grid search.
    """

    def __init__(
        self,
        gammas: list = None,
        etas: list = None,
        xis: list = None,
        N: int = None,
        seed: int = None,
        show_progress: bool = True,
    ):
        self.gammas = gammas
        self.etas = etas
        self.xis = xis
        self.N = N
        self.seed = seed
        self.show_progress = show_progress
        if seed is not None:
            np.random.seed(seed)
        if N is None:
            raise ValueError("N must be specified for grid search.")

GridSearchClassification

Bases: GridSearch

Grid search implementation for Bayesian logistic regression using HoLMC samplers.

This class evaluates sampler performance over a grid of parameters using predictive accuracy based on samples averaged over time.

Methods

run(X, y, lamb): Executes the grid search and returns a DataFrame sorted by maximum accuracy. compute_accuracy(X, y, samples): Computes predictive accuracy from the sample sequence.

Source code in holmc/utils/gridsearch.py 
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class GridSearchClassification(GridSearch):
    """
    Grid search implementation for Bayesian logistic regression using HoLMC
    samplers.

    This class evaluates sampler performance over a grid of parameters using
    predictive accuracy
    based on samples averaged over time.

    Methods
    -------
    run(X, y, lamb):
        Executes the grid search and returns a DataFrame sorted by maximum
        accuracy.
    compute_accuracy(X, y, samples):
        Computes predictive accuracy from the sample sequence.
    """

    def compute_accuracy(self, X, y, samples):
        """
        Compute classification accuracy over cumulative average of sampled
        parameters.

        Parameters
        ----------
        X : np.ndarray
            Feature matrix of shape (n_samples, n_features).
        y : np.ndarray
            Binary target labels (0 or 1) of shape (n_samples,).
        samples : np.ndarray
            Array of sampled parameter vectors of shape (n_samples, n_features)

        Returns
        -------
        np.ndarray
            Array of accuracy scores as function of the sample index.
        """
        n = samples.shape[0]
        accuracies = []

        for i in range(1, n + 1):
            avg_theta = np.mean(samples[:i], axis=0)
            logits = X @ avg_theta
            probs = sigmoid(logits)
            y_pred = (probs >= 0.5).astype(int)
            acc = accuracy(y, y_pred)
            accuracies.append(acc)

        return np.array(accuracies)

    def run(self, X: np.ndarray, y: np.ndarray, lamb: float = None):
        """
        Run the grid search for classification.

        Parameters
        ----------
        X : np.ndarray
            Feature matrix of shape (n_samples, n_features).
        y : np.ndarray
            Binary target labels (0 or 1) of shape (n_samples,).
        lamb : float
            Regularization (prior precision) parameter. Required.

        Returns
        -------
        pd.DataFrame
            DataFrame containing the grid search results sorted by maximum
            accuracy.
        """
        if lamb is None:
            raise ValueError("lamb must be specified for grid search.")

        results = []
        N = self.N

        is_third_order = self.xis is not None

        for eta in tqdm(self.etas, disable=not self.show_progress, desc="Eta"):
            for gamma in self.gammas:
                xi_list = self.xis if is_third_order else [None]
                for xi in xi_list:
                    try:
                        if is_third_order:
                            params = O3Params(eta=eta, gamma=gamma, xi=xi)
                            sampler = HoLMCSamplerO3Classification(
                                params=params,
                                N=N,
                                seed=self.seed,
                                show_progress=False,
                            )
                        else:
                            params = O4Params(eta=eta, gamma=gamma)
                            sampler = HoLMCSamplerO4Classification(
                                params=params,
                                N=N,
                                seed=self.seed,
                                show_progress=False,
                            )
                        samples = sampler.sample(X, y, lamb)
                        ac = self.compute_accuracy(X, y, samples)
                        max_acc = np.nanmax(ac)

                        result = {
                            "gamma": gamma,
                            "eta": eta,
                            "MaxAcc": max_acc,
                        }
                        if is_third_order:
                            result["xi"] = xi
                        results.append(result)
                    except Exception:
                        result = {"gamma": gamma, "eta": eta, "MaxAcc": np.nan}
                        if is_third_order:
                            result["xi"] = xi
                        results.append(result)

        self.results_df = pd.DataFrame(results).sort_values(
            "MaxAcc", ascending=False
        )
        return self.results_df

compute_accuracy(X, y, samples)

Compute classification accuracy over cumulative average of sampled parameters.

Parameters

X : np.ndarray Feature matrix of shape (n_samples, n_features). y : np.ndarray Binary target labels (0 or 1) of shape (n_samples,). samples : np.ndarray Array of sampled parameter vectors of shape (n_samples, n_features)

Returns

np.ndarray Array of accuracy scores as function of the sample index.

Source code in holmc/utils/gridsearch.py 
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def compute_accuracy(self, X, y, samples):
    """
    Compute classification accuracy over cumulative average of sampled
    parameters.

    Parameters
    ----------
    X : np.ndarray
        Feature matrix of shape (n_samples, n_features).
    y : np.ndarray
        Binary target labels (0 or 1) of shape (n_samples,).
    samples : np.ndarray
        Array of sampled parameter vectors of shape (n_samples, n_features)

    Returns
    -------
    np.ndarray
        Array of accuracy scores as function of the sample index.
    """
    n = samples.shape[0]
    accuracies = []

    for i in range(1, n + 1):
        avg_theta = np.mean(samples[:i], axis=0)
        logits = X @ avg_theta
        probs = sigmoid(logits)
        y_pred = (probs >= 0.5).astype(int)
        acc = accuracy(y, y_pred)
        accuracies.append(acc)

    return np.array(accuracies)

run(X, y, lamb=None)

Run the grid search for classification.

Parameters

X : np.ndarray Feature matrix of shape (n_samples, n_features). y : np.ndarray Binary target labels (0 or 1) of shape (n_samples,). lamb : float Regularization (prior precision) parameter. Required.

Returns

pd.DataFrame DataFrame containing the grid search results sorted by maximum accuracy.

Source code in holmc/utils/gridsearch.py 
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def run(self, X: np.ndarray, y: np.ndarray, lamb: float = None):
    """
    Run the grid search for classification.

    Parameters
    ----------
    X : np.ndarray
        Feature matrix of shape (n_samples, n_features).
    y : np.ndarray
        Binary target labels (0 or 1) of shape (n_samples,).
    lamb : float
        Regularization (prior precision) parameter. Required.

    Returns
    -------
    pd.DataFrame
        DataFrame containing the grid search results sorted by maximum
        accuracy.
    """
    if lamb is None:
        raise ValueError("lamb must be specified for grid search.")

    results = []
    N = self.N

    is_third_order = self.xis is not None

    for eta in tqdm(self.etas, disable=not self.show_progress, desc="Eta"):
        for gamma in self.gammas:
            xi_list = self.xis if is_third_order else [None]
            for xi in xi_list:
                try:
                    if is_third_order:
                        params = O3Params(eta=eta, gamma=gamma, xi=xi)
                        sampler = HoLMCSamplerO3Classification(
                            params=params,
                            N=N,
                            seed=self.seed,
                            show_progress=False,
                        )
                    else:
                        params = O4Params(eta=eta, gamma=gamma)
                        sampler = HoLMCSamplerO4Classification(
                            params=params,
                            N=N,
                            seed=self.seed,
                            show_progress=False,
                        )
                    samples = sampler.sample(X, y, lamb)
                    ac = self.compute_accuracy(X, y, samples)
                    max_acc = np.nanmax(ac)

                    result = {
                        "gamma": gamma,
                        "eta": eta,
                        "MaxAcc": max_acc,
                    }
                    if is_third_order:
                        result["xi"] = xi
                    results.append(result)
                except Exception:
                    result = {"gamma": gamma, "eta": eta, "MaxAcc": np.nan}
                    if is_third_order:
                        result["xi"] = xi
                    results.append(result)

    self.results_df = pd.DataFrame(results).sort_values(
        "MaxAcc", ascending=False
    )
    return self.results_df

GridSearchRegression

Bases: GridSearch

Grid search implementation for Bayesian linear regression using HoLMC samplers.

This class runs over a grid of (eta, gamma, xi) parameters and evaluates performance using the Wasserstein-2 distance between the sampled distribution and the target posterior.

Methods

run(X, y, lamb): Executes the grid search and returns a DataFrame of results sorted by W2 distance.

Source code in holmc/utils/gridsearch.py 
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class GridSearchRegression(GridSearch):
    """
    Grid search implementation for Bayesian linear regression using HoLMC
    samplers.

    This class runs over a grid of (eta, gamma, xi) parameters and evaluates
    performance
    using the Wasserstein-2 distance between the sampled distribution and the
    target posterior.

    Methods
    -------
    run(X, y, lamb):
        Executes the grid search and returns a DataFrame of results sorted by
        W2 distance.
    """

    def run(self, X: np.ndarray, y: np.ndarray, lamb: float = None):
        """
        Run the grid search for regression.

        Parameters
        ----------
        X : np.ndarray
            Design matrix of shape (n_samples, n_features).
        y : np.ndarray
            Response vector of shape (n_samples,) or (n_samples, 1).
        lamb : float
            Regularization (prior precision) parameter. Required.

        Returns
        -------
        pd.DataFrame
            DataFrame containing the grid search results sorted by minimum
            Wasserstein-2 distance.
        """
        if lamb is None:
            raise ValueError("lamb must be specified for grid search.")

        if X is None or y is None:
            raise ValueError("X and y must be provided for grid search.")

        N = self.N

        results = []

        is_third_order = self.xis is not None

        for eta in tqdm(self.etas, disable=not self.show_progress, desc="Eta"):
            for gamma in self.gammas:
                xi_list = self.xis if is_third_order else [None]
                for xi in xi_list:
                    try:
                        if is_third_order:
                            params = O3Params(eta=eta, gamma=gamma, xi=xi)
                            sampler = HoLMCSamplerO3Regression(
                                params=params,
                                N=N,
                                seed=self.seed,
                                show_progress=False,
                            )
                        else:
                            params = O4Params(eta=eta, gamma=gamma)
                            sampler = HoLMCSamplerO4Regression(
                                params=params,
                                N=N,
                                seed=self.seed,
                                show_progress=False,
                            )
                        samples = sampler.sample(X, y, lamb)
                        metric = Wasserstein2Distance(X=X, y=y)
                        dist = metric.w2distance(samples)
                        min_dist = np.nanmin(dist)

                        result = {
                            "gamma": gamma,
                            "eta": eta,
                            "w2dist": min_dist,
                        }
                        if is_third_order:
                            result["xi"] = xi
                        results.append(result)
                    except Exception:
                        result = {"gamma": gamma, "eta": eta, "w2dist": np.nan}
                        if is_third_order:
                            result["xi"] = xi
                        results.append(result)

        self.results_df = pd.DataFrame(results).sort_values("w2dist")
        return self.results_df

run(X, y, lamb=None)

Run the grid search for regression.

Parameters

X : np.ndarray Design matrix of shape (n_samples, n_features). y : np.ndarray Response vector of shape (n_samples,) or (n_samples, 1). lamb : float Regularization (prior precision) parameter. Required.

Returns

pd.DataFrame DataFrame containing the grid search results sorted by minimum Wasserstein-2 distance.

Source code in holmc/utils/gridsearch.py 
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def run(self, X: np.ndarray, y: np.ndarray, lamb: float = None):
    """
    Run the grid search for regression.

    Parameters
    ----------
    X : np.ndarray
        Design matrix of shape (n_samples, n_features).
    y : np.ndarray
        Response vector of shape (n_samples,) or (n_samples, 1).
    lamb : float
        Regularization (prior precision) parameter. Required.

    Returns
    -------
    pd.DataFrame
        DataFrame containing the grid search results sorted by minimum
        Wasserstein-2 distance.
    """
    if lamb is None:
        raise ValueError("lamb must be specified for grid search.")

    if X is None or y is None:
        raise ValueError("X and y must be provided for grid search.")

    N = self.N

    results = []

    is_third_order = self.xis is not None

    for eta in tqdm(self.etas, disable=not self.show_progress, desc="Eta"):
        for gamma in self.gammas:
            xi_list = self.xis if is_third_order else [None]
            for xi in xi_list:
                try:
                    if is_third_order:
                        params = O3Params(eta=eta, gamma=gamma, xi=xi)
                        sampler = HoLMCSamplerO3Regression(
                            params=params,
                            N=N,
                            seed=self.seed,
                            show_progress=False,
                        )
                    else:
                        params = O4Params(eta=eta, gamma=gamma)
                        sampler = HoLMCSamplerO4Regression(
                            params=params,
                            N=N,
                            seed=self.seed,
                            show_progress=False,
                        )
                    samples = sampler.sample(X, y, lamb)
                    metric = Wasserstein2Distance(X=X, y=y)
                    dist = metric.w2distance(samples)
                    min_dist = np.nanmin(dist)

                    result = {
                        "gamma": gamma,
                        "eta": eta,
                        "w2dist": min_dist,
                    }
                    if is_third_order:
                        result["xi"] = xi
                    results.append(result)
                except Exception:
                    result = {"gamma": gamma, "eta": eta, "w2dist": np.nan}
                    if is_third_order:
                        result["xi"] = xi
                    results.append(result)

    self.results_df = pd.DataFrame(results).sort_values("w2dist")
    return self.results_df