We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regul…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,932 papers · 148 categories
Trend · papers per month
48 results for “divergence-measure fields”
Extends BV functions and divergence-measure fields to metric spaces.
problem Defining BV functions and divergence-measure fields in metric spaces.
method Employing differential structure developed by N. Gigli, extending BV functions and divergence-measure fields to metric spaces.
result Gauss-Green formulas established for BV functions and divergence-measure fields in metric spaces.
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 -divergence measures improve robustness in noisy label learning.
problem Improving robustness in learning with noisy labels.
method Derived decoupling property of -divergence measures under label noise.
result Properly defined -divergence measures are robust with label noise.
Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univa…
Unified approach for sample aggregation in transfer learning across various divergence measures.
problem Optimizing sample aggregation from source to target distributions for improved target performance.
method Unified algorithmic approach that adapts to multiple divergence measures via a weak modulus of transfer.
result Unified approach achieves near optimal rates in terms of the unknown strong modulus, applicable in more general settings.
Statistical Properties and Power Analysis of Divergence Measures for Credit Risk Model Monitoringq-fin.ST
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.
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the sa…
We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants…
Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergen…
Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical results show that the efficiency of DA algorithms depends on their capacity of …
Geometric framework analyzes bias in variational inference for posterior functionals.
problem Analyzing the bias of posterior functionals under variational approximations.
method Developed a geometric framework to evaluate the bias of posterior functionals using the variational tangent space.
result The leading-order bias of a posterior functional is determined by its component orthogonal to the variational tangent space.
A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable l…
Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data, designing divergence measure that is interpretable and can handle high-dimensiona…
The paper studies properties of spaces and their boundaries.
problem Understanding the boundary structure and unit normal on spaces.
method Proves concentration of boundary measure, discusses localization of unit normal, and develops tools for perimeter minimizers.
result Proves that the boundary measure of sets with finite perimeter is concentrated on the -regular set .
We propose a direct estimation method for Rényi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets and , respectively with and samples, where is a constant value. Considering the -nearest neighbor (-NN) graph of in the j…
Proposes a new divergence measure for probability distributions.
problem Challenges in estimating divergences from empirical samples.
method Embeds data into RKHS, computes Jensen-Shannon divergence between covariance operators.
result Establishes RJSD as a lower bound on Jensen-Shannon divergence, enabling variational estimation.
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov ch…
The paper explores how information theory aids in statistical learning models.
problem Characterizing fundamental performance limits in statistical learning models.
method Introduces divergence measures and evidence lower bound (ELBO) in model training.
result Provides a systematic derivation for generative diffusion models.
This paper reviews recent advancements in amortized Variational Inference.
problem Scalability and efficiency issues in traditional Variational Inference.
method Systematic review of various Variational Inference techniques, focusing on amortized approaches.
result Amortized Variational Inference improves scalability and efficiency for generative modeling tasks.
New divergence measures improve KL approximation.
problem Improving KL divergence approximation without AC condition.
method Introduced -geodesical skew divergence.
result Properties of -geodesical skew divergence studied.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
The objective of change-point detection is to discover abrupt property changes lying behind time-series data. In this paper, we present a novel statistical change-point detection algorithm based on non-parametric divergence estimation between time-series samples from two retrospective segments. Our method uses the rela…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that previous methods for measuring this radius, e.g. relative entropy or polynomial diverg…
We introduce a novel framework for adversarial training where the target distribution is annealed between the uniform distribution and the data distribution. We posited a conjecture that learning under continuous annealing in the nonparametric regime is stable irrespective of the divergence measures in the objective fu…
The paper interprets DRO problems through chance constraints, offering a clearer business interpretation.
problem Understanding distributional ambiguity in optimization problems.
method Relating DRO problems to mean-deviation problems and chance-constrained optimization.
result A DRO problem can be transformed into a chance-constrained optimization problem, providing a clearer interpretation.
Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent attention models over possibly large external memory modules constitute the core m…
In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be described by a Bayesian network that evolve dynamically over time and the observ…
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and -divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper …
Improved UDA framework using -divergence measures.
problem Addressing distribution shifts in machine learning.
method Refined -divergence-based discrepancy and -domain discrepancy.
result Novel target error and sample complexity bounds.
Causal KL improves on existing metrics for evaluating causal models.
problem Insufficient discrimination between causal models using edit-distance and KL divergence.
method Introducing Causal KL, an augmented KL divergence that considers causal relationships.
result Causal KL variants effectively distinguish between observationally equivalent models.
Automates VI divergence selection for efficient few-shot learning.
problem Efficiently selecting divergence measures for VI to improve performance.
method Meta-learning algorithm to learn optimal divergence metric and variational parameter initialization.
result Meta-learning approach outperforms standard VI methods across various tasks.
Automated feature selection is important for text categorization to reduce the feature size and to speed up the learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the Information Theory, which aims to rank the features with their discriminative capacity…
New model learns better policies from expert demonstrations with higher efficiency.
problem Learning accurate policies from expert demonstrations with high efficiency.
method Generative adversarial imitation learning (GAIL) model that learns -divergence automatically.
result Learns better policies with higher data efficiency in physics-based control tasks.
Learning from multiple sources of information is an important problem in machine-learning research. The key challenges are learning representations and formulating inference methods that take into account the complementarity and redundancy of various information sources. In this paper we formulate a variational autoenc…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…
A new algorithm learns diverse policies in reinforcement learning.
problem Learning diverse behaviors in reinforcement learning.
method Proposes Maximum Entropy Diverse Exploration (MEDE) algorithm.
result The set of policies learned by MEDE capture the same modalities as the optimal maximum entropy policy.
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating t…
Paper proposes a method to monitor research topic evolution.
problem Difficulty in tracking research topic diffusion and evolution.
method Deep Non-negative Autoencoder with information divergence measurement.
result Identifies evolution of research topics and discovers topic diffusions.
The paper improves semi-supervised learning using -divergences and -Rényi divergences.
problem Improving semi-supervised learning with noisy pseudo-labels.
method Inspired by -divergences and -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.
TAROT enhances robustness and domain adaptability with domain-invariant features.
problem Developing models robust to adversarial attacks across diverse domains.
method Derives a new generalization bound and proposes TAROT algorithm.
result TAROT outperforms state-of-the-art methods in accuracy and robustness.
Discriminative calibration: Check Bayesian computation from simulations and flexible classifierstat.ML
Proposes a new method to improve Bayesian computation accuracy using flexible classification.
problem Bayesian computations accuracy check using rank-based simulation-based calibration has limitations.
method Replaces marginal rank test with a flexible classification approach that learns from data.
result Improves statistical power and provides an interpretable divergence measure of miscalibration.
Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if considered with respect to suitable noise statistics. However, the noise in reconstr…
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased import…
Unified deep metric learning approach using neural networks.
problem Learning embeddings of data and extending Euclidean distances.
method Deep Bregman divergences based on neural networks.
result Superior performance on benchmark datasets compared to existing methods.
Unified framework for deriving generalization bounds in supervised learning.
problem Generalization error bounds in supervised learning.
method Data Processing Inequality PAC-Bayesian framework.
result Unified bounds on binary Kullback-Leibler generalization gap for various divergences.
Bayesian learning has been recently considered as an effective means of accounting for uncertainty in trained deep network parameters. This is of crucial importance when dealing with small or sparse training datasets. On the other hand, shallow models that compute weighted sums of their inputs, after passing them throu…
Paper improves MMD estimation for analytical mean embeddings.
problem Improving MMD estimation for distributions with analytical mean embeddings.
method Proposes a tighter concentration result for MMD estimation under semi-explicit settings and extends to unbounded kernels.
result Demonstrates efficiency in real-world applications like index replication and calibration.