The paper improves risk bounds for maximum likelihood estimation with arbitrary penalties.
problem Improving risk bounds for maximum likelihood estimation with arbitrary penalties.
method Developed a more general inequality for arbitrary penalties, leading to exact risk bounds of order 1/n.
result Derived exact risk bounds of order 1/n for iid parametric models, improving on previous bounds.
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
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.
The study uses information theory to set lower bounds on model likelihoods.
problem Improving latent variable models by optimizing priors or likelihoods.
method Applying rate-distortion theory to find lower bounds on negative log likelihood.
result Rate-distortion theory can be used to optimize priors and likelihoods in latent variable models.
The paper tightens the upper bound on likelihood of finite mixtures.
problem Non-convexity and local maxima in finite mixture models.
method Convex optimization to find a tight upper bound on likelihood.
result A tight convex upper bound on the likelihood of a finite mixture can be computed.
New variational bounds improve posterior covariances and likelihoods.
problem Improving variational inference with different divergence measures.
method Applying variational perturbation theory to construct new variational bounds.
result New variational bounds lead to more accurate posterior covariances and higher likelihoods.
Link between PAC-Bayesian bounds and Bayesian marginal likelihood.
problem Understanding the connection between frequentist and Bayesian approaches in risk minimization.
method Exhibit a strong link between PAC-Bayesian risk bounds and Bayesian marginal likelihood, especially for the negative log-likelihood loss function.
result PAC-Bayesian minimization maximizes Bayesian marginal likelihood, providing an alternative to Bayesian Occam's razor.
Derives M2VAE objective from marginal joint log-likelihood.
problem Training Multi-Modal Variational Autoencoders (M2VAEs). method Derives trainable evidence lower bound from marginal joint log-likelihood.
result Derives M2VAE objective from marginal joint log-likelihood. This paper introduces a method to estimate log-likelihood in VAE models.
problem Difficulty in comparing models trained via ELBO due to lack of log-likelihood.
method Introduces a general upper bound to approximate model evidence.
result Efficiently approximates model evidence and compares to other bounds.
We extend Bayes' theorem for upper probabilities considering likelihood uncertainty.
problem Addressing uncertainty in likelihood for upper probability bounds.
method Generalization of Wasserman and Kadane's result, considering both prior and likelihood uncertainty.
result A sufficient condition for the upper bound to become an equality.
New model generates graphs with tighter likelihood bounds and better quality.
problem Intractable likelihood of autoregressive graph models.
method Derive exact joint probability, approximate node orderings, variational inference.
result Lower bound on log-likelihood is significantly tighter than previous methods.
New method improves model training on sequential data.
problem Training latent variable models with ELBO limits.
method Introducing FIVO, a family of tighter bounds.
result FIVO leads to substantial improvements over ELBO.
New lower bounds improve logistic log-likelihood optimization and inference.
problem Designing computationally tractable lower bounds for logistic log-likelihoods.
method Developed a piece-wise quadratic lower bound that uniformly improves tangent quadratic minorizers.
result Improves the speed of convergence and accuracy of variational Bayes approximations.
We simplify inference for TPP models with latent structures.
problem Intractable marginalization in TPP models with latent structures.
method Approximate inference over latent variables using a tight upper bound on the approximation gap.
result Improved results for models like Survival Analysis.
Paper quantifies label shift robustly.
problem Quantifying label shift in datasets.
method Robust estimators of label distribution.
result Maximum Likelihood Estimator is a robust estimator.
This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
A new method estimates marginal likelihoods with high accuracy.
problem Difficult high-dimensional summation or integration problem in computing marginal likelihood.
method Bidirectional Monte Carlo, using stochastic lower and upper bounds.
result Estimates marginal likelihoods with high probability between stochastic bounds.
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n and arbitrary f. Study tensor completion for tensors with sparse CP factors under noisy conditions.
problem Noisy tensor completion for tensors with a sparse CP factor.
method Complexity-regularized maximum likelihood principle and ADMM-type algorithm.
result General theoretical error bounds and validation via experiments.
New bounds for DPPs avoid spectral decomposition and enable inference.
problem Learning parameters of DPPs' kernel K is difficult due to spectral decomposition and intractable normalizing constant. method Derive cheap bounds on likelihood without spectral decomposition, enabling variational and MCMC inference.
result Cheap variational and moderately expensive MCMC inference methods for DPPs.
Bayesian neural networks with data augmentation show a persistent cold posterior effect.
problem Understanding the cold posterior effect in Bayesian neural networks with data augmentation.
method Developed principled Bayesian neural networks using data augmentation, providing exact likelihoods and tight bounds.
result The cold posterior effect persists even in models incorporating data augmentation, suggesting it's not an artifact.
Study shows how to reduce variational inference bias by concentrating likelihood ratio distribution.
problem Bias and variance issues in variational inference.
method Upper bound variational gap using dispersion measure of likelihood ratio, suggesting methods to reduce bias.
result Reducing bias in variational inference can be achieved by making likelihood ratio distribution more concentrated.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The original approach to approximate inference in these models used variational compressio…
Improves latent variable use in generative models.
problem Poor use of latent variables in variational autoencoders (VAEs).
method Combines data log likelihood with autoencoder reconstruction likelihood.
result Ensures latent variable captures observation information and generates well.
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.
New bounds improve training of VAEs on noisy data.
problem Training Variational AutoEncoders on noisy data.
method Proposes Kullback-Leibler and Rényi divergence bounds for log-likelihood.
result Numerically stable training without extra noise.
New method uses approximate KLD for intractable likelihood models.
problem Designing experiments for models with intractable likelihoods.
method Derive a lower bound of KLD utility, express it in terms of entropies, and evaluate efficiently.
result Demonstrated the performance of the proposed method through numerical examples.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.
problem Dequantization gap in modeling discrete data like images.
method Introducing subset flows to allow exact computation of likelihoods for discrete data.
result PixelCNN models trained with exact likelihood computation achieve state-of-the-art results on CIFAR-10.
This work connects GANs and VAEs by computing sample likelihoods in GANs.
problem Lack of explicit probability models in GANs limits their use in statistical inference.
method Construct an explicit probability model for GANs, proving they maximize a variational lower-bound on average sample log likelihoods.
result Wasserstein GANs with entropy regularization can compute sample likelihoods, bridging GANs and VAEs.
New framework for tracking varying bounds in time series forecasting.
problem Forecasting bounded time series with varying bounds.
method Extended log-likelihood estimation, online maximum likelihood estimation, Normalized Gradient Descent (NGD) for quasiconvex optimization.
result Derive an Online Normalized Gradient Descent algorithm for online bound tracking.
The paper sets sample complexity bounds for identifying LTI systems from a finite set.
problem Identifying an LTI system from a finite set of possible systems using trajectory data.
method Maximum likelihood estimator and information theory tools.
result Upper and lower bounds for sample complexity are derived, independent of stability assumption.
Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.
problem Quantum machine learning's loss minimization through cross entropy is affected by measurement outcomes.
method Defined quantum cross entropy, proved its lower bounds, and investigated its relation to quantum fidelity and likelihood.
result Quantum cross entropy is lower-bounded by negative log-likelihood when derived from quantum data, but measurement outcomes can cause loss.
The paper introduces multimodal generative models to improve data marginal likelihood.
problem Improving data marginal likelihood in multimodal settings.
method Derives variational bounds on the evidence for multimodal deep generative models, generalizes objectives for different model types, and benchmarks across various datasets.
result Multimodal VAEs excel in image, label, and text datasets with and without weak supervision.
Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We discuss howtree-width is in many ways the appropriate measure of complexity and…
We establish conditions for maximum likelihood consistency in time series models.
problem Invertibility conditions often fail in empirical observation-driven models.
method Derive weaker conditions for maximum likelihood consistency.
result Consistency of maximum likelihood estimator holds for various models.
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.
Gaussian prior and likelihood improve bandit learning performance.
problem Improving bandit learning with misspecified Gaussian distributions.
method An agent with a bounded information ratio interacts with a Bernoulli bandit based on a Gaussian prior and likelihood.
result The regret increase is at most linear in the square-root of the time horizon for diffuse distributions.
Estimates policy value from off-policy data in contextual bandits.
problem Estimating policy value from limited off-policy data in contextual bandits.
method Empirical likelihood techniques for optimization.
result Improves over previous methods in finite sample regimes.
A new method simplifies variational inference for complex models.
problem Challenges in exact Bayesian inference due to intractable integrals.
method Rewriting the lower bound on model log-likelihood using a finite sample of Gaussian latent variables.
result Demonstrated effectiveness on synthetic and real-world examples.
Synthesizes sensor likelihoods to enforce accuracy constraints in uncertain systems.
problem Designing sensing architectures for systems with uncertain or unavailable sensor models and accuracy requirements.
method Inverts the design flow, synthesizing measurement likelihoods that minimize Kullback-Leibler divergence from the prior while enforcing an accuracy bound.
result The method synthesizes a maximum-entropy posterior and induced likelihood, accommodating various discrepancy metrics.
Directly estimates Fisher score for likelihood maximization.
problem Intractable likelihood functions with model simulations.
method Gradient-based optimization using local score matching and linear parameterization.
result Efficient approximation of Fisher score improves likelihood maximization.
Optimally tackles covariate shift in RKHS-based nonparametric regression.
problem Covariate shift in nonparametric regression over RKHS.
method Two families of covariate shift problems defined using likelihood ratios. Minimax rate-optimal estimators for KRR and reweighted KRR.
result KRR is minimax rate-optimal and strictly sub-optimal compared to naive estimator under covariate shift.
Paper analyzes active learning for maximum likelihood estimation.
problem Active learning for maximum likelihood estimation.
method Two-stage active learning algorithm for maximum likelihood estimation.
result Single extra round of interaction is sufficient for near-optimal performance.
Sparse multinomial logistic regression for multiclass classification with feature selection.
problem High-dimensional multiclass classification with a focus on sparse models.
method Penalized maximum likelihood with complexity penalty, feature selection using group Lasso and Slope classifiers.
result Achievement of minimax order in both small and large number of classes regimes.
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.
Proposes learning invariances in neural networks using a weight-space approach.
problem Learning invariances from data in neural networks remains an open problem.
method Minimizes a lower bound on the marginal likelihood in weight space.
result Results in higher performing models with naturally learned invariances.