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.
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.
In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equival…
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.
Survival regression method improves log-likelihood scores.
problem Improper scoring rules in survival regression models.
method SurvivalMonotonic-net (SuMo-net) with monotonic neural networks.
result SuMo-net achieves state-of-the-art log-likelihood scores.
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. 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.
Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 con…
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.
Noise-Contrastive Estimation improves efficiency for estimating log-likelihood of complex point processes.
problem Estimating log-likelihood of complex multivariate point processes is computationally expensive.
method Noise-Contrastive Estimation adapted for multivariate point processes, with provable guarantees.
result Our method achieves similar log-likelihood with fewer evaluations and less time.
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.
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.
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.
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. 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.
Recent work in variational inference (VI) uses ideas from Monte Carlo estimation to tighten the lower bounds on the log-likelihood that are used as objectives. However, there is no systematic understanding of how optimizing different objectives relates to approximating the posterior distribution. Developing such a conn…
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.
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.
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.
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…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the max…
SPRT-TANDEM improves sequential classification accuracy with fewer samples.
problem Efficiently classifying sequential data with high accuracy and low sampling cost.
method Deep neural network-based SPRT algorithm that estimates log-likelihood ratio of two hypotheses.
result SPRT-TANDEM achieves statistically significantly better classification accuracy than other classifiers with fewer samples.
A new base distribution for normalizing flows allows modeling complex distributions without sacrificing invertibility.
problem Normalizing flows struggle with complex, non-trivial distributions.
method Learned rejection sampling for base distribution, combined with optimization of log-likelihood and Kullback-Leibler divergence.
result The method effectively models complicated distributions without sacrificing invertibility.
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields…
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…
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.
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.
Though with progress, model learning and performing posterior inference still remains a common challenge for using deep generative models, especially for handling discrete hidden variables. This paper is mainly concerned with algorithms for learning Helmholz machines, which is characterized by pairing the generative mo…
Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition functions, and often yields quite accurate results. However, AIS is prone to ov…
We explain SSL objectives as log-likelihoods in a data curation model.
problem Lack of understanding of SSL objectives as log-likelihoods.
method Formulate SSL objectives as a log-likelihood in a generative model of data curation.
result SSL methods can be understood as lower-bounds on a principled log-likelihood.
RWR converges to global optimum in certain settings.
problem Proving convergence of RWR to optimal policy.
method Iterative learning with return-weighted log-likelihood.
result RWR converges to global optimum under certain conditions.
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.
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 …
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…
New framework trains Schrödinger Bridge models using SDEs for generative tasks.
problem Unclear relation between SB optimization and modern generative model training.
method Forward-Backward SDEs theory for likelihood training of SB models.
result Training algorithm achieves comparable results on image generation datasets.
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.
wd1 improves reasoning in dLLMs by optimizing policies without policy ratios.
problem Improving reasoning in diffusion-based large language models through RL.
method wd1: ratio-free policy optimization using weighted log-likelihood.
result wd1 outperforms diffusion-based GRPO while requiring lower computational cost.
This work evaluates deep generative models using RD curves, providing a more comprehensive quality assessment.
problem Quantitative evaluation of deep generative models is challenging, especially for implicit models.
method Proposes using rate distortion (RD) curves to evaluate and compare deep generative models, approximating the entire curve with similar computations to log-likelihood estimation.
result Approximating the entire RD curve provides a more comprehensive quality assessment than scalar-valued metrics.
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, the best estimator performance is not always achieved with this penalty. The …
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
problem Optimizing parameters of finite mixture models of Bernoulli and categorical distributions.
method Mean Field Games theory applied to multi-population systems.
result The Mean Field Games approach provides a method to compute mixture model parameters.
Enhances VAEs for sharper image synthesis.
problem Blurriness in generated images from VAEs.
method Integrates a downscaled version of the original image into the VAE framework and uses it as input to the decoder.
result Improves FID score in image synthesis while maintaining similar log-likelihood performance.
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.
This work gives an in-depth derivation of the trainable evidence lower bound obtained from the marginal joint log-Likelihood with the goal of training a Multi-Modal Variational Autoencoder (M2VAE).
Paper introduces new methods for modeling categorical data.
problem Training generative models on categorical data like text and segmentation.
method Argmax Flows and Multinomial Diffusion models.
result Models outperform existing methods in log-likelihood.
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 …
In this work, a deep learning-based method for log-likelihood ratio (LLR) lossy compression and quantization is proposed, with emphasis on a single-input single-output uncorrelated fading communication setting. A deep autoencoder network is trained to compress, quantize and reconstruct the bit log-likelihood ratios cor…
We introduce the multiresolution recurrent neural network, which extends the sequence-to-sequence framework to model natural language generation as two parallel discrete stochastic processes: a sequence of high-level coarse tokens, and a sequence of natural language tokens. There are many ways to estimate or learn the …
In healthcare, the highest risk individuals for morbidity and mortality are rarely those with the greatest modifiable risk. By contrast, many machine learning formulations implicitly attend to the highest risk individuals. We focus on this problem in point processes, a popular modeling technique for the analysis of the…