New method minimizes robust density power-based divergences for general parametric densities.
problem Computational complexity of minimizing DPD for general parametric densities.
method Stochastic approach to minimize DPD for general parametric density models.
result Proposed method can be applied to minimize other density power-based γ-divergences.
This work extends t-SNE to f-divergences for better visualization of data.
problem Visualizing high-dimensional data with improved accuracy and structure capture.
method Extending t-SNE to f-divergences, analytically and empirically evaluating different types of latent structure.
result Different f-divergences perform better for different types of latent structure.
New algorithm improves topic modeling for short texts.
problem Inference of latent topics from short texts is challenging.
method Developed a stochastic divergence minimization algorithm for Biterm Topic Model (BTM).
result The new algorithm estimates latent topics more accurately and efficiently.
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Paper introduces f-divergence variational inference for broader application.
problem Variational inference limited to specific divergences.
method Generalizes variational inference to all f-divergences using f-divergence minimization.
result Unified framework for variational inference with arbitrary f-divergences.
New methods minimize GFlowNet training divergences for better sampling.
problem Training GFlowNets with KL divergence leads to biased and high-variance estimators.
method Design and implement efficient estimators for four divergence measures.
result Properly minimizing these divergences yields a provably correct and effective training scheme.
New algorithm reduces error in regression problems.
problem Minimizing composite objective functions with quadratic and convex components.
method Stochastic dual averaging with constant step-size, proving convergence rate O(1/n).
result Extends least-squares regression to various convex regularizers and geometries.
New bounds found for optimizing non-convex functions with noisy data.
problem Limits of first-order stochastic optimization in non-convex settings.
method Divergence decomposition to construct challenging subclasses.
result Sharp lower bounds on noisy gradient queries for various non-convex classes.
Study compares statistical properties and power of divergence measures for credit risk monitoring.
problem Detecting distributional shifts in credit risk models.
method Derives statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence, demonstrating their applicability in credit risk monitoring.
result Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal practical trade-offs in minimizing false positives vs. detecting changes.
Unified reinforcement learning and stochastic processes with action-driven processes.
problem Combining reinforcement learning and stochastic processes for efficient control.
method Action-driven processes, leveraging control-as-inference, and minimizing Kullback-Leibler divergence.
result Action-driven processes unify reinforcement learning and stochastic processes, equivalent to maximum entropy reinforcement learning.
Bayesian neural networks improve reinforcement learning in complex systems.
problem Learning policies in stochastic dynamical systems with complex dynamics.
method Combines Bayesian neural networks with random roll-outs and stochastic optimization.
result Demonstrates improved performance in challenging benchmarks and real-world applications.
New method improves neural spike train models by minimizing divergence directly, leading to better performance.
problem Poor performance and divergence issues in spike train models using maximum likelihood estimation.
method Directly minimize maximum mean discrepancy using spike train kernels and stochastic optimization.
result The proposed method generates well-behaved models with better control over feature trade-offs.
Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-α scales to large datasets because it can be implemented using stochastic gradient descent. BB-α can be applied to complex probabilistic models with little effort since it only requires as input the likel…
Optimizes diffusion processes for target distributions.
problem Efficiently generating target distributions from point masses.
method Stochastic interpolant framework with conditional expectation drift.
result Optimal diffusion coefficient minimizes path-space KL divergence.
Agents learn from a continuum of hypotheses to minimize divergence.
problem Learning from a continuum of hypotheses with limited data.
method Distributed learning with stochastic mirror descent.
result Non-asymptotic bounds for concentration of beliefs.
Paper formalizes and analyzes a new bound for variational inference.
problem Lack of theoretical guarantees in variational algorithms.
method Introduces VR-IWAE bound, a generalization of IWAE.
result VR-IWAE bound leads to unbiased gradient estimators.
Optimal probability measure found for constrained stochastic processes.
problem Finding optimal probability measure with constraints for stochastic processes.
method Existence and uniqueness proof, explicit measure change, optimal drift and compensator adjustments.
result Explicit form of the optimal measure change and characterisation of adjustments.
The paper evaluates biased methods for alpha-divergence minimization.
problem The impact of bias on solutions found for alpha-divergence minimization.
method Empirical evaluation of biased methods for alpha-divergence minimization, focusing on bias effects and dimensionality.
result Solutions are biased towards KL-divergence minimizers and require impractical computation in high dimensions to minimize alpha-divergence.
Jeffreys Flow improves robustness of Boltzmann generators for rare event sampling.
problem Rare events and metastable trapping in sampling physical systems with rough energy landscapes.
method Introduces Jeffreys Flow, a robust generative framework using Parallel Tempering distillation and symmetric Jeffreys divergence to mitigate mode collapse and improve mode coverage.
result Minimizing Jeffreys divergence suppresses mode collapse and corrects inaccuracies in multi-modal distributions.
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
Stochastic Gradient Descent approximates Bayesian inference.
problem Approximating Bayesian posterior distributions efficiently.
method Constant SGD with parameter tuning and momentum.
result Constant SGD can approximate posterior distributions with minimized KL divergence.
Improved machine learning method estimates entropy production robustly.
problem Estimating entropy production from trajectory data.
method Variational representation of α-divergence loss functions. result Optimal α=−0.5 yields best performance. Study dynamics of alternating minimization for bilinear regression under large system limits.
problem Understanding the time evolution of alternating minimization for bilinear regression.
method Replica method applied to a multi-temperature glassy system.
result Dynamics of alternating minimization can be described by a two-dimensional discrete stochastic process.
Estimates Schrödinger potentials with minimal sample size.
problem Estimating Schrödinger potentials for generative modeling.
method Empirical Kullback-Leibler risk minimizer over log-potentials.
result Excess KL-risk decreases as fast as O(log2n/n). Stochastic Gradient Descent (SGD) is analyzed for probabilistic modeling.
problem Optimizing hyperparameters in probabilistic models.
method Interpreting SGD as a continuous-time stochastic process and minimizing Kullback-Leibler divergence.
result Optimal SGD parameters can match the posterior distribution.
Stochastic neural networks use Gaussian noise with monotonic activation functions.
problem Training RBM with non-linearities.
method Laplace approximation with Gaussian noise for monotonic activation functions.
result Exp-RBM learns useful representations using stochastic units.
GANs can learn without always minimizing a divergence, contrary to recent theories.
problem The need for GANs to minimize a divergence at every step is overly restrictive.
method Empirical counterexamples and gradient penalties.
result GANs can learn distributions without always minimizing a specific divergence.
New method improves variational inference for better posterior approximation.
problem Challenges in minimizing inclusive KL divergence for amortized variational inference.
method Likelihood-tempered sequential Monte Carlo samplers to estimate inclusive KL gradient.
result SMC-Wake method fits variational distributions more accurately than existing methods.
New theory explains GAN's high quality but low diversity.
problem Lack of theoretical justification for non-saturating GAN training.
method Showed non-saturating GAN training approximately minimizes a specific f-divergence.
result Non-saturating GAN training minimizes a particular f-divergence.
We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL dive…
A new DC programming approach improves RBM training efficiency.
problem Improving the training efficiency of Restricted Boltzmann Machines (RBMs).
method Formulated a stochastic DC programming approach to minimize RBM log-likelihood.
result The new algorithm achieves higher log-likelihood more rapidly with the same computational budget.
ERM with f-divergence regularization yields unique solution.
problem Optimizing empirical risk with f-divergence. method Mild conditions on f lead to unique optimal measure. result Equivalence of ERM-fDR to different f-divergence regularization. New method minimizes f-divergence for better imitation learning.
problem Learning from multi-modal demonstrations, especially interpolating between modes.
method Minimizing reverse KL divergence or I-projection for any f-divergence.
result Our method reliably imitates multi-modal behaviors better than existing methods.
Paper proposes robust and sparse GLM regression using stochastic optimization.
problem Sparse GLM's lack robustness against outliers in high-dimensional data.
method Robust and sparse linear regression based on γ-divergence with stochastic optimization. result The proposed method outperforms existing methods in numerical experiments and real data analysis.
EL_2O improves posterior inference without sampling noise.
problem Statistical inference of analytically non-tractable posteriors.
method Expectation optimization of L_2 distance squared between approximate and true posteriors.
result EL_2O provides a reliable estimate of posterior quality and converges rapidly.
GANs can generate realistic data without minimizing a divergence, contrary to current theory.
problem Current theory suggests GANs minimize a divergence to generate realistic data.
method Discussed various loss functions for G, showing they are not divergences and do not have the same equilibrium.
result GANs can use a wide range of loss functions, not just divergences, to generate realistic data.
The paper defines minimal norm tensors for curvature and divergence tensors, explaining Weyl and Cotten tensors.
problem Understanding curvature tensors and their minimal norm.
method Analyzing minimal norm tensors for third and fourth covariant tensors, including Riemannian curvature and divergence.
result Weyl tensor and Cotten tensor are identified as minimal norm tensors of Riemannian curvature and divergence tensors, respectively.
New framework improves variational inference with Markov chain methods.
problem Challenges of minimizing KL divergence with stochastic gradient descent.
method Markov chain score ascent (MCSA) methods, including parallel MCSA (pMCSA).
result Improved theoretical and empirical performance of MCSA methods.
This paper introduces a new method to interpolate between MCMC and variational inference.
problem The tradeoff between accuracy and efficiency in MCMC and variational inference methods.
method Derives a distribution over variational parameters to minimize divergence, and provides sampling methods.
result A new method that interpolates between MCMC and variational inference, improving efficiency.
New method improves adversarial robustness of neural networks.
problem Vulnerability of neural networks to adversarial attacks.
method Integrates φ-divergence regularization into distributionally robust risk function.
result Achieves near-optimal sample complexity with efficient stochastic gradient methods.
Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution. As a side effect, these approximations yield significantly different biases and…
Unbiased methods for alpha-divergence minimization struggle in high dimensions.
problem The difficulty of unbiased alpha-divergence minimization in high dimensions.
method Signal-to-Noise Ratio (SNR) analysis of gradient estimators.
result The SNR of the gradient estimator worsens exponentially with dimensionality.
A new algorithm using sliced Wasserstein distance improves GMM parameter estimation.
problem Inefficiency of EM algorithm in finding optimal GMM parameters.
method Proposes a new algorithm using sliced Wasserstein distance to minimize the distance between the mixture model and data distribution.
result The new algorithm yields more robust and accurate GMM parameter estimates.
A new metric measures time series divergence efficiently.
problem Quantifying subtle differences in time series data.
method Sequence Likelihood (SL) divergence, a generalized KL divergence for time series.
result Efficient estimators of SL divergence from finite sample paths.
The paper tightens bounds for estimating Schrödinger potentials in unpaired data translation.
problem Estimating Schrödinger potentials in unpaired data translation.
method Using stochastic optimal control and Ornstein-Uhlenbeck process, the paper derives tight bounds on the generalization ability of an empirical risk minimizer.
result The approach achieves almost optimal convergence rates for Gaussian mixtures.
Unified framework for analyzing convergence of RSAs using Wasserstein divergence.
problem Analyzing convergence of constant stepsize recursive stochastic algorithms (RSAs).
method Lifting RSA into a higher-dimensional space as a Markov chain and studying the distribution's contraction property with respect to Wasserstein divergence.
result RSAs' iterates' distribution converges to an invariant distribution under certain contraction properties.
Proposes an online method for solving non-convex DRO with KL regularization.
problem Solving distributionally robust optimization with non-convex objectives.
method Practical online stochastic methods for DRO with KL regularization, avoiding high-dimensional dual variables and online learning issues.
result Empirical studies show significant speedup and efficiency in training deep learning models.
Optimal control theory connects diffusion models to generative modeling.
problem Sampling from unnormalized densities in statistics and computational sciences.
method Deriving a Hamilton-Jacobi-Bellman equation and applying control theory to minimize Kullback-Leibler divergence.
result Time-reversed diffusion sampler (DIS) outperforms other diffusion-based sampling methods.