EM algorithm converges to global max in latent Gaussian tree models.
problem Optimizing log-likelihood in latent Gaussian tree models.
method Analyzed the optimization landscape and convergence of EM algorithm.
result EM algorithm converges to global maximum in latent Gaussian tree models.
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method is used to form the noisy log-likelihood estimates using computationally costly …
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the forme…
We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using …
This work links SOMs and GMMs, providing a mathematical basis for their use.
problem Understanding the relationship between SOMs and GMMs.
method Mathematical treatment showing SOMs as gradient descent on a GMM log-likelihood.
result SOMs can be interpreted as probabilistic models, justifying their use in various applications.
Sparse matrices simplify computation of GP variances and likelihoods.
problem Efficient computation of posterior variance and log-likelihood for additive Matérn GPs.
method Represented posterior mean, variance, log-likelihood, and gradient using sparse matrices.
result Efficient computation of posterior mean, variance, log-likelihood, and gradient in O(nlogn) time. Framework for Bayesian inference using GP emulated MH sampler for noisy likelihoods.
problem Approximate Bayesian inference with limited noisy log-likelihood evaluations.
method Gaussian process emulates MH sampler for log-likelihood evaluations; sequential experimental design selects evaluation points.
result Approximate sampler is sample-efficient and robust to GP assumptions.
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid …
Improves sequence modeling with a flow-based recurrent mixture density network.
problem Sequence modeling and sequence-to-sequence mapping applications.
method Generalized recurrent mixture density networks using normalized flow transformations.
result Significantly improved fit to image sequences measured by log-likelihood.
ELU algorithm improves on EM for over-specified Gaussian mixtures.
problem Slow convergence of EM in over-specified Gaussian mixtures.
method Developed ELU algorithm for two-component mixtures, combining exponential location update and gradient descent.
result ELU converges to final statistical radius after logarithmic iterations, resolving open question.
The MAP estimate's log-likelihood sub-optimality is hard to bound in general.
problem Bounding the expected log-likelihood sub-optimality of MAP for exponential families.
method Interpreting MAP as stochastic mirror descent and analyzing convergence rates.
result Current convergence results do not apply to standard examples of exponential families.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
A new MFG framework for evolving clusters from Gaussian mixtures.
problem Evolutionary clustering of time-dependent Gaussian mixtures.
method Control-theoretic framework based on Mean Field Games (MFG) with coupled HJB and Fokker-Planck systems.
result MFG dynamics recover classical EM algorithm trajectories with mass conservation.
Study reveals structure of local minima in GMMs, identifying key cluster centers.
problem Identifying optimal cluster centers in non-convex GMM landscapes.
method Analyzing the negative log-likelihood function of GMMs in the population limit.
result Local minima share a common structure that partially identifies true cluster centers.
The log-likelihood loss in heteroscedastic neural networks can lead to poor parameter estimates.
problem Capturing aleatoric uncertainty in deep learning models.
method Examine the log-likelihood loss in conjunction with gradient-based optimizers and propose an alternative formulation, β-NLL. result Using an appropriate β largely mitigates the issue of poor parameter estimates. We consider the problem of aligning a pair of databases with jointly Gaussian features. We consider two algorithms, complete database alignment via MAP estimation among all possible database alignments, and partial alignment via a thresholding approach of log likelihood ratios. We derive conditions on mutual informatio…
The paper optimizes designs for distinguishing between Gaussian process models.
problem Discriminating between two Gaussian process models.
method Sequential and static design criteria, including Kullback Leibler divergences and log-likelihood ratios.
result Necessary conditions for optimal design measures are provided.
A scalable algorithm for GP regression selects relevant covariates efficiently.
problem Scalable variable selection in large GP regression models.
method VGPR algorithm using Vecchia approximation for sparse precision matrix, mini-batch subsampling.
result Improved scalability and accuracy in selecting relevant covariates.
Introduces a new theoretical framework for exponential smoothing.
problem Theoretical foundation and robustness of simple exponential smoothing.
method Stochastic gradient ascent to optimize Gaussian log-likelihood functions.
result Simple exponential smoothing converges to the trend of a trend-stationary process.
Unified analysis for graph learning from multi-attribute Gaussian time series.
problem Estimating conditional independence graph from multi-attribute Gaussian time series data.
method Unified theoretical analysis using a penalized log-likelihood objective function in the frequency domain.
result Established sufficient conditions for consistency and graph recovery in high-dimensional settings.
A new model predicts discrete events with flexible, nonparametric baseline and excitation.
problem Limited flexibility in discrete Hawkes models for event prediction.
method Gaussian Process Discrete Hawkes Process (GP-DHP) with collapsed latent representation.
result Improves predictive log-likelihood for diverse event patterns.
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approach for this task. We begin by introducing a surprising connection between the graphical lasso and hi…
Square-root natural-gradient improves variational inference convergence.
problem Challenges in establishing theoretical convergence guarantees for natural-gradient descent.
method Square-root parameterization for Gaussian covariance.
result Establishes novel convergence guarantees for natural-gradient Gaussian inference.
Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.
problem Finding Lagrange multipliers for Maximum-Entropy distributions is computationally challenging.
method Employed Gaussian processes to approximate the Lagrange multipliers as a map of moments. Optimized hyperparameters by maximizing log-likelihood.
result Data-driven Maximum-Entropy closure performs well in approximating non-equilibrium distributions.
Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The dra…
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which c…
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…
The paper uses Tukey g-and-h neural networks for non-Gaussian data regression.
problem Regression with non-Gaussian data.
method Training neural networks to predict Tukey g-and-h distribution parameters via negative log-likelihood minimization.
result Efficiency demonstrated in simulated and real-world datasets.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
Test log-likelihood comparisons can be misleading.
problem Misinterpretation of test log-likelihood in model comparison.
method Simple examples of model comparison and forecast accuracy.
result Test log-likelihood does not always correlate with model accuracy.
Autotune optimizes Lasso tuning parameters efficiently and accurately.
problem Efficiently selecting Lasso tuning parameters in high-dimensional models.
method Alternates optimizing regression coefficients and noise standard deviation.
result Autotune outperforms existing methods in low signal-to-noise regimes.
Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
DGMEs use Gaussian mixtures to quantify uncertainty in deep learning.
problem Quantifying uncertainty in complex predictive densities.
method DGMEs use a Gaussian mixture model with an EM algorithm for parameter learning.
result DGMEs outperform state-of-the-art models in uncertainty quantification.
Predict covariance from features using convex optimization.
problem Predicting the covariance of a Gaussian vector from another feature vector.
method A generalized linear model with convex optimization for fitting parameters.
result Predicted covariance matrices are symmetric positive definite.
This paper proposes a method to improve VAEs by extracting latent spaces from pre-trained diffusion models.
problem VAEs struggle with generating high-quality images due to unrealistic Gaussian assumptions.
method Optimizes an encoder to maximize marginal data log-likelihood and derives a decoder analytically.
result The method enhances VAE performance by discarding Gaussian assumptions and training a separate decoder network.
New ZIPLN model accounts for zero-inflation in multivariate count data.
problem Zero-inflation in multivariate count data.
method Introduced Zero-Inflated PLN (ZIPLN) model with variational inference.
result ZIPLN significantly improves log-likelihood and reduces dispersion.
New method estimates causal structure from sparse data.
problem Inferring causal structure from sparse observational data.
method Log-likelihood of sparsely mixed ICA with penalty terms.
result Proposed method outperforms existing methods.
A new Metropolis-Hastings algorithm uses Gaussian Processes to speed up sampling from complex models.
problem Sampling from computationally expensive probabilistic models.
method Two-stage Metropolis-Hastings algorithm with a Gaussian Process surrogate model.
result The approach learns the target distribution while sampling, eliminating the need for pre-training.
Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.
problem State estimation in systems with noisy measurements and non-Gaussian noise.
method Recursive KalmanNet uses a recurrent neural network to estimate states with consistent error covariance, optimizing for Gaussian negative log-likelihood.
result Recursive KalmanNet outperforms conventional Kalman filters and deep learning-based estimators in non-Gaussian noise conditions.
A new VIS approach improves log-likelihood estimation in latent variable models.
problem Challenges in achieving high log-likelihood with VI for complex posterior distributions.
method Uses forward χ2 divergence to optimize proposal distribution for better log-likelihood estimation. result Consistently outperforms state-of-the-art baselines in log-likelihood and parameter estimation.
Proposes a robust similarity measure for sparse time series data.
problem Sparse time course data in biological settings.
method Gaussian processes (GP) similarity measure based on log-likelihood ratio.
result Enhanced robustness to noise compared to Euclidean distance.
New method optimizes clustering with better log-likelihood landscape.
problem Nonconvex log-likelihood optimization in model-based clustering.
method Entropic optimal transport loss for Sinkhorn-EM algorithm.
result New loss function avoids spurious local optima.
In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during training. Variational Autoencoders (VAE) are one important example where variation…
New method calculates DMN log-likelihood faster.
problem Precise and fast computation of DMN log-likelihood.
method Derived a closed form expression using gamma function properties.
result Closed form calculation is faster with same accuracy.
Neural Boltzmann Machines improve on CRBMs for modeling data.
problem Limited expressivity of CRBMs with noisy data.
method Convert CRBM parameters to neural networks.
result NBMs can approximate data likelihood better.
Algorithm samples composite logconcave densities efficiently.
problem Sampling from composite logconcave densities efficiently.
method Uses a restricted Gaussian oracle and gradient queries.
result Achieves strong total variation distance guarantees.
A new KDE model prevents singular solutions and accelerates optimization for probabilistic modeling.
problem Adapting to varying densities in data regions for probabilistic modeling.
method Adaptive KDE model with individual bandwidths, LOO-MLL criterion, and modified EM algorithm.
result The proposed models prevent singular solutions and have promising performance.