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.
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…
Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative model) and a discriminator (a teacher providing training signal) that each minimize t…
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. 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.
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.
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.
DAIS minimizes symmetrized KL divergence between initial and target distributions.
problem Optimizing over initial distributions in importance sampling.
method Differentiable annealed importance sampling (DAIS) minimizing symmetrized KL divergence.
result DAIS minimizes symmetrized KL divergence between initial and target distributions.
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.
Paper proposes f-DPG for aligning language models with preferences.
problem Aligning language models with user preferences.
method Uses f-divergence to approximate target distributions and minimizes a forward KL from it using DPG.
result Jensen-Shannon divergence often outperforms forward KL divergence, leading to significant improvements.
Paper presents ERM with f-divergence regularization and its properties.
problem Minimizing empirical risk with f-divergence constraints. method Introduces normalization function and solves ERM-fDR via ODE. result Characterizes difference between empirical risks and provides numerical algorithm.
DM framework improves robustness and efficiency in latent-mixture models.
problem Efficient and robust inference in latent-mixture models.
method Divergence-minimization framework with monotonic convergence and robustness guarantees.
result DM yields consistent and asymptotically normal estimators under correct specification.
New method improves imitation learning from expert observations.
problem Challenges in imitation learning from observation setting.
method Reparameterized Variational Divergence Minimization.
result Our method outperforms baseline approaches in low-dimensional tasks.
Generative adversarial networks (GANs) can be interpreted as an adversarial game between two players, a discriminator D and a generator G, in which D learns to classify real from fake data and G learns to generate realistic data by "fooling" D into thinking that fake data is actually real data. Currently, a dominating …
Paper shows robust generative learning with minimal assumptions on target distributions.
problem Learning generative models with minimal assumptions on target distributions.
method Lipschitz-regularized α-divergences with minimal assumptions. result Stable learning across various target distributions with minimal assumptions.
New algorithm speeds up NMF with β-divergence.
problem Efficiently factorize nonnegative matrices with β-divergence. method Joint majorization-minimization with multiplicative updates.
result Significant reduction in computation time for NMF.
We address the problem of imitation learning with multi-modal demonstrations. Instead of attempting to learn all modes, we argue that in many tasks it is sufficient to imitate any one of them. We show that the state-of-the-art methods such as GAIL and behavior cloning, due to their choice of loss function, often incorr…
Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks, alternative non-likelihood training criteria have been proposed. Whilst not necessarily…
The Dirichlet mechanism protects privacy while minimizing KL divergence.
problem Minimizing KL divergence while protecting sensitive data privacy.
method Using the exponential mechanism with the KL divergence loss function, resulting in the Dirichlet mechanism.
result Proved a probability tail bound on KL divergence and derived a lower bound for sample complexity.
The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this work, we propose extending this method to other f-divergences. We analytically a…
New method learns disentangled signals without prior or model constraints.
problem Learning disentangled signals from data without prior or model constraints.
method Minimizes conditional KL divergence using a sequential algorithm to learn de-mixing flow models.
result Method learns self-sufficient signals that can reconstruct missing values.
New method estimates velocity fields for minimizing f-divergences without overfitting.
problem Minimizing statistical discrepancies between target and particle distributions.
method Directly estimate velocity fields using interpolation techniques, proving consistency under mild conditions.
result Consistent estimators of velocity fields improve accuracy in applications like domain adaptation and missing data imputation.
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.
We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how…
A new differentiable divergence for time series comparison.
problem Computing discrepancies between time series of varying lengths.
method Proposed a new divergence, soft-DTW divergence, addressing issues of differentiability and positivity.
result Showed that the new divergence is a valid divergence: non-negative and minimized when time series are equal.
Dual optimization connects ERM-fDR to normalization function.
problem Empirical risk minimization with f-divergence regularization.
method Dual formulation, Legendre-Fenchel transform, implicit function theorem, nonlinear ODE.
result Computational method to calculate normalization function efficiently.
New analysis of annealing paths in sampling and estimation.
problem Sampling from complex distributions and estimating normalization constants.
method Extending known results on Bregman divergence to quasi-arithmetic means under monotonic embedding.
result Analogous result for quasi-arithmetic means, highlighting the interplay between means, parametric families, and divergence functionals.
New measures generalize existing ones, linking information and risk.
problem Linking information measures and risk in statistical decision problems.
method Introducing new families of divergence measures and deriving an information processing equality.
result Extension of variational φ-divergence representation to multiple distributions. New ONMF model minimizes KL divergence for better sparse data modeling.
problem Clustering and data modeling with sparse vectors.
method Developed KL-ONMF algorithm based on alternating optimization.
result KL-ONMF outperforms Frobenius-norm ONMF for document classification and hyperspectral image unmixing.
New samplers minimize KL divergence for constrained and non-Euclidean geometries.
problem Efficient sampling from constrained and non-Euclidean distributions.
method Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent.
result New samplers converge more rapidly and accurately than prior methods.
Gradient flows of neural networks converge to optimal values or diverge, with thresholds and asymptotic behaviors.
problem Understanding the convergence and divergence of gradient flows in neural networks.
method Analysis of gradient flows on loss landscapes of neural networks using o-minimal structures.
result Gradient flows either converge to optimal values or diverge to infinity, with thresholds and asymptotic behaviors.
f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
A study on α-GANs proving convergence and estimation guarantees.
problem Analyzing the convergence and estimation guarantees of α-GANs. method Proved a correspondence between α-GANs and f-divergences, and provided estimation bounds. result Estimation bounds indicate diverse GAN behavior as a function of α. t-SNE algorithm's points remain bounded under gradient flow.
problem Understanding the boundedness of t-SNE points.
method Gradient flow of t-SNE with KL divergence, examining weak convergence assumptions.
result Points generated by t-SNE remain bounded under gradient flow.
Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distrib…
The paper improves semi-supervised learning using f-divergences and α-Rényi divergences.
problem Improving semi-supervised learning with noisy pseudo-labels.
method Inspired by f-divergences and α-Rényi divergences, the paper develops new empirical risk functions and regularization techniques. result The new methods show better performance than traditional self-training methods, especially in noisy pseudo-label scenarios.
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the po…
We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equival…
We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a fam…
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothn…
New guarantees for VI in symmetric cases, extending previous results.
problem Symmetry in variational inference for complex distributions.
method Analysis of f-divergences and their stationary points under symmetry. result Symmetry-matching principles ensure recovery of mean and correlation matrix.
Proposes a method to prevent overfitting in deep DRE models.
problem Overfitting in deep DRE models using empirical Bregman divergence.
method Introduces a non-negative correction for empirical Bregman divergence.
result The proposed method mitigates train-loss hacking and improves performance.
Improved Bayesian inference using power priors with historical data.
problem Improving Bayesian inference with historical data.
method Generalized power priors that adapt to the α parameter of Amari's α-divergence. result Improved performance through appropriate choices of the α parameter. MonoFlow rethinks GANs using Wasserstein gradient flows.
problem Inconsistencies between GAN theory and practice.
method Unified generative modeling framework based on Wasserstein gradient flows.
result Adversarial training can be seen as particle flow optimization.
Unified framework for debiased machine learning using Riesz representer and Bregman divergence.
problem Estimating causal and structural parameters in machine learning.
method Generalized Riesz regression for fitting Riesz representer via Bregman divergence minimization.
result Automatic covariate balancing and Neyman orthogonality properties for debiased estimation.
This note proves that any locally extremal non-self-conjugate geodesic loop in a Riemannian manifold is a closed geodesic. As a consequence, any complete and non-contractible Riemannian manifold with diverging injectivity radii along diverging sequences and without points conjugate to themselves, possesses a minimizing…
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative …