Paper develops unbiased gradient estimator for continuous-time models.
problem Estimating unbiased gradient of log-likelihood for continuous-time models.
method Doubly randomized scheme with coupled conditional particle filter (CCPF).
result Unbiased gradient estimate facilitates gradient-based algorithms.
Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
A new method normalizes EBM training by introducing a learnable parameter.
problem Training energy-based models with maximum likelihood is challenging due to intractable normalisation constants.
method Proposes a self-normalised log-likelihood (SNL) objective that introduces a learnable parameter representing the normalisation constant.
result The SNL objective is a lower bound of the log-likelihood and can be directly optimised using stochastic gradient techniques.
By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of th…
Gradient boosting adapted for vector inputs.
problem Applying gradient boosting to multi-class classification problems.
method Extended gradient boosting framework to vector inputs using histogram-based decision trees.
result Efficient algorithm for vector-valued objectives.
New bounds show BBVI's gradient variance matches SGD conditions, improving parameterization efficiency.
problem Understanding and improving the convergence of black-box variational inference (BBVI).
method Showed BBVI satisfies matching gradient variance bounds corresponding to the ABC condition for smooth and quadratically-growing log-likelihoods.
result Proven BBVI's gradient variance matches SGD conditions, with superior dimensional dependence for mean-field parameterization.
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. 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. Maximum likelihood estimation of energy-based models is a challenging problem due to the intractability of the log-likelihood gradient. In this work, we propose learning both the energy function and an amortized approximate sampling mechanism using a neural generator network, which provides an efficient approximation o…
This paper improves SNN training by using multiple sample compartments.
problem Training SNNs with single-sample estimators leads to inaccurate log-likelihood estimates.
method Proposes a GEM-based online learning algorithm that uses multiple independent spiking signals.
result Significant improvements in log-likelihood, accuracy, and calibration with multiple compartments.
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.
Method infers parameters in complex diffusion processes.
problem Parameter inference in high-dimensional, non-linear diffusion processes.
method Differentiable score matching to approximate diffusion bridges, used in an importance sampler.
result Numerically stable framework for parameter inference and diffusion mean estimation.
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We exp…
New method uses joint stochastic approximation to improve learning of discrete latent models.
problem Challenges in learning discrete latent variable models, especially with inference model gradients and log-likelihood optimization.
method Proposes a new method based on stochastic approximation theory that directly maximizes the target log-likelihood and minimizes the posterior-inference model divergence.
result Consistently outperforms recent competitive algorithms in generative modeling and structured prediction tasks.
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
GBHT uses gradient boosting for density estimation with theoretical guarantees.
problem Density estimation for unsupervised learning.
method Gradient Boosting Histogram Transform (GBHT) with Negative Log Likelihood loss.
result GBHT achieves faster convergence rates and better performance than base learners in density estimation.
Quantum annealer speeds up RBM training for image classification.
problem Training RBM with contrastive divergence (CD) is slow and computationally expensive.
method Used D-Wave 2000Q quantum annealer to calculate model expectation of gradient learning for RBM.
result Quantum training yields similar classification performance to CD but faster.
Learning RBMs using standard algorithms such as CD(k) involves gradient descent on the negative log-likelihood. One of the terms in the gradient, which involves expectation w.r.t. the model distribution, is intractable and is obtained through an MCMC estimate. In this work we show that the Hessian of the log-likelihood…
NNNH uses neural networks to model complex event patterns.
problem Analyzing multi-dimensional nonlinear Hawkes processes with mutual excitation and inhibition.
method NNNH employs feedforward neural networks to model individual kernels and base intensity, optimizing parameters via Stochastic Gradient Descent.
result NNNH accurately captures complexities of nonlinear Hawkes processes, as demonstrated by numerical experiments.
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.
DisARM improves gradient estimation for binary latent variables.
problem Challenges in training models with discrete latent variables.
method Uses antithetic sampling over continuous augmentation.
result DisARM consistently outperforms ARM and baseline methods in log-likelihood and variance.
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.
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.
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
Proves error bounds for PGD, extending log-Sobolev and Talagrand inequalities.
problem Maximum likelihood estimation of large latent variable models.
method Extending log-Sobolev and Talagrand inequalities to models with strongly concave log-likelihoods.
result Non-asymptotic error bounds for PGD in models satisfying LSI and PŁI.
Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias ca…
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message pas…
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.
Generative adversarial networks (GANs) are a powerful approach to unsupervised learning. They have achieved state-of-the-art performance in the image domain. However, GANs are limited in two ways. They often learn distributions with low support---a phenomenon known as mode collapse---and they do not guarantee the exist…
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.
A novel quantum model improves RBM performance and is efficiently trainable.
problem Improving the performance of RBM models.
method Quantum model with parametrically coupled fermions to classical signals.
result The model outperforms classical RBM with the same number of hidden units.
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.
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-co…
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.
NRWS improves training of SBNs and HMs using natural gradient.
problem Training Sigmoid Belief Networks and Helmholtz Machines efficiently.
method Exploits block-diagonal structure of Fisher Information Matrices to use natural gradient.
result NRWS and NBiHM achieve better log-likelihood and faster convergence.
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.
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.
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is numerically very challenging. We address this challenge by developing a new adaptive…
We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural…
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.
Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al. 2016, Maddison et al. 2016) has taken a different approach, introducing a continuou…
A new method for Bayesian inference in high dimensions using projected Stein variational gradient descent.
problem Bayesian inference challenges in high-dimensional data.
method Adapting Stein variational gradient descent to exploit intrinsic low dimensionality of data.
result pSVGD is more accurate and efficient than SVGD, especially in high-dimensional settings.
Federated CTMC model estimates bridge deterioration hazards without sharing raw data.
problem Bridge inspection data privacy and cross-organizational data sharing constraints.
method Federated CTMC hazard model with local optimization and FedAvg aggregation.
result Federated model converges on global benchmark parameters without data transfer.
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approximation of the covariance matrix despite, the fact that these mat…
New method tracks time-varying parameters in data.
problem Tracking unknown time-varying parameters in data.
method Stochastic gradient descent-based recursive scheme with log-likelihood as gain function.
result Convergence in mean-square error in a suitable neighborhood of the unknown parameter.
IBS efficiently estimates log-likelihood without bias.
problem Estimating log-likelihood for complex models.
method Inverse Binomial Sampling (IBS) for efficient, unbiased estimation.
result IBS produces lower error in estimated parameters and maximum log-likelihood values.
The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is ver…
Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likel…