We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.
problem Traditional generative models struggle with heavy-tailed and multivariate data, leading to unstable training and mode dropping.
method We extend the invariant statistical loss method to handle heavy-tailed and multivariate data using a Pareto-ISL generator trained with input noise from a generalised Pareto distribution.
result Pareto-ISL accurately models the tails of heavy-tailed distributions while capturing central characteristics.
Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and injecting noise during training naturally bias the network towards learning invari…
ScoreStop uses gradient tests to stop gradient boosting early.
problem Overfitting in gradient boosted decision trees.
method ScoreStop uses a functional score test based on gradients to stop boosting.
result ScoreStop is competitive with loss-based early stopping methods.
New method trains generative models without discriminators, improving stability and accuracy.
problem Training implicit generative models with adversarial discriminators leads to instability and mode-dropping.
method Invariant statistical loss function, avoiding discriminators.
result Successfully trains generative models for various complex distributions without mode-dropping.
Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…
Extends LOSS invariant naturality to positive contact surgeries.
problem Naturality of LOSS invariant under positive contact surgeries.
method Proves naturality of LOSS invariant for Legendrian knots under positive integer contact surgeries.
result Contact invariant of +n surgery depends only on classical invariants of S.
Improves statistical learning bounds with self-concordant losses.
problem Statistical prediction with nuisance components.
method Orthogonal statistical learning with self-concordant loss.
result Non-asymptotic bounds on excess risk improved by a dimension factor.
The paper examines statistical properties of IL and LVR in automated market makers.
problem Assessing the performance of automated market makers and their profitability.
method Analysis of random walk properties and statistical integral combined with CFMM mechanics.
result IL and LVR have identical expectation values but different distribution functions for Brownian motion.
Study anti-invariant submersions from holomorphic statistical manifolds.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. Thi…
Paper analyzes statistical properties of log-cosh loss function.
problem No statistical analysis of log-cosh loss function in literature.
method Presented statistical properties of log-cosh loss function, compared to Cauchy distribution, and examined various statistical procedures.
result Characterized statistical properties of log-cosh loss function, including distribution, likelihood function, and Fisher information.
New framework controls statistical dispersion for high-stakes applications.
problem Understanding and controlling the dispersion of loss distributions in high-stakes applications.
method Simple yet flexible framework for distribution-free control of statistical dispersion measures.
result Proposed methods control statistical dispersion measures with societal implications.
Polyak step size GD reaches final radius of convergence after log iterations.
problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.
CurvSSL improves SSL by aligning local manifold curvature.
problem Improving self-supervised learning by capturing local manifold geometry.
method CurvSSL augments Barlow Twins with a curvature-based regularizer to align and decorrelate embeddings across augmentations.
result Curvature-regularized SSL yields competitive or improved linear evaluation performance.
Study excess risk in statistical inference with transformations.
problem Excess risk in estimating random variables from feature vectors and transformations.
method Characterize lossless transformations, develop test statistics, and information-theoretic bounds.
result Strongly consistent partitioning test statistic for lossless transformations.
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter. It was shown by Juditsky and Nemirovski (2009) that when the $\ell_2…
As regulators pay more attentions to losses rather than gains, we are able to derive a new class of risk statistics, named regulator-based risk statistics with scenario analysis in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou et al. \ci…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of su…
This research focuses on invariant probabilistic predictions, showing they are not robust under distribution shifts.
problem The challenge of creating robust probabilistic predictions that remain consistent under distribution shifts.
method A causality-inspired framework to investigate invariance and robustness of probabilistic predictions with respect to proper scoring rules.
result Arbitrary distribution shifts do not admit invariant and robust probabilistic predictions, unlike point predictions.
This paper studies moduli spaces of statistical structures on Lie groups.
problem Understanding statistical structures on Lie groups.
method Introduced and studied moduli spaces for left-invariant statistical structures on Lie groups.
result Moduli spaces of left-invariant Riemannian metrics are singletons for certain Lie groups.
Develops a new theory of loss functions for statistical machine learning.
problem Evaluation of solutions in binary and multiclass classification problems.
method Defines loss functions as subgradients of support functions of convex sets, enabling a calculus of losses.
result Provides a novel perspective on losses and develops a calculus that interpolates between different losses.
Study invariant connections on multivariate Gaussian distributions.
problem Understanding statistical connections on multivariate Gaussian distributions.
method Investigate invariant connections on N0n with the Fisher metric. result Explicitly determined invariant connections and their moduli spaces.
Study improves PM concentration forecasting using MCCR loss.
problem Forecasting particulate matter concentration in South Korea.
method Used MCCR loss for regression analysis of air pollution and weather data.
result MCCR loss is more effective for extreme value forecasting.
We show that the EH class and the LOSS invariant of Legendrian knots in contact 3-manifolds are functorial under regular Lagrangian concordances in Weinstein cobordisms. This gives computable obstructions to the existence of regular Lagrangian concordances.
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
Improved computational complexity in statistical models using second-order information.
problem Polynomial convergence of gradient descent in singular statistical models.
method Normalized Gradient Descent (NormGD) algorithm with second-order information.
result NormGD reaches final statistical radius in logarithmic iterations of n. New algorithm for robust high-dimensional linear regression is both fast and statistically optimal.
problem Challenges in high-dimensional linear regression under heavy-tailed noise or outliers.
method Projected sub-gradient descent algorithm for sparse and low-rank regression problems.
result Algorithm achieves linear convergence and statistical optimality under various noise conditions.
We study proper losses for discrete generative models without knowing the target distribution.
problem Evaluating generative models in the discrete setting without direct access to the target distribution.
method Define and construct black-box proper losses using statistical estimation theory.
result Black-box proper losses must be of polynomial form and involve more samples than the polynomial degree.
New method optimizes portfolios for non-stationary markets.
problem Inadequate classical portfolio optimization for non-stationary markets.
method Reformulate portfolio optimization in spectral domain, using complex statistics.
result Time-varying optimal capital allocations for non-stationary markets.
This paper quantifies privacy loss in exploratory data analysis.
problem Privacy loss in exploratory data analysis is often overlooked in privacy budgets.
method Quantitative analysis of privacy loss for statistical functions.
result Privacy loss must be considered in calculating machine learning privacy budgets.
Monge SAM improves deep learning by making sharpness-aware minimization invariant to reparametrizations.
problem Non-invariance of sharpness-aware minimization (SAM) to reparametrizations.
method Introduces Monge SAM, a reparametrization-invariant version of SAM using a Riemannian metric.
result Monge SAM enhances robustness and generalization compared to previous methods.
A new algorithm improves both computational efficiency and statistical optimality for robust low-rank matrix and tensor estimation.
problem Challenges in low-rank matrix estimation under heavy-tailed noise, both computationally and statistically.
method Riemannian sub-gradient (RsGrad) algorithm, which is computationally efficient and statistically optimal.
result RsGrad achieves linear convergence and statistical optimality for robust loss functions under Gaussian and heavy-tailed noise.
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
The paper explores IL and LVR in AMMs, identifying three regimes and the effect of fees.
problem The relationship between impermanent loss and loss-versus-rebalancing in AMMs.
method Statistical analysis, focus on fees, block times, and continuous time limit.
result Three regimes identified: identical, distinct distribution functions, and distinct averages.
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
Generalized algorithm for translation and scale-invariant prediction.
problem Sequential prediction with expert advice, focusing on translation and scale invariance.
method Designing a generalized online algorithm using the universal prediction perspective to compete against a generic class of expert selection strategies.
result No preliminary knowledge of loss sequences is required; performance bounds are stable under arbitrary scalings and translations.
Flexible framework for bounding high-loss predictions using quantiles.
problem Need for rigorous guarantees in risk-sensitive applications.
method Order statistics of loss values, flexible quantile-based metrics.
result Ability to rigorously control loss quantiles on real-world datasets.
The well known domain shift issue causes model performance to degrade when deployed to a new target domain with different statistics to training. Domain adaptation techniques alleviate this, but need some instances from the target domain to drive adaptation. Domain generalisation is the recently topical problem of lear…
Score matching offers efficient estimation for certain distributions.
problem Estimating probability distributions with intractable constants.
method Score matching as an alternative to maximum likelihood.
result Score matching is computationally and statistically efficient for certain distributions.
New algorithm handles bandit problems under translations and scales.
problem Adversarial multi-armed bandit problems with arbitrary translations and scales.
method Innovative online algorithm invariant to translations and scales, using universal prediction.
result Second-order regret bounds, unaffected by affine transformations of losses.
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
problem Characterizing geometric properties of contact CR-submanifolds in Sasakian statistical manifolds.
method Characterization of integrability of invariant and anti-invariant distributions, development of results on specific types of contact CR submanifolds, introduction of statistical contact CR-product.
result Introduction of a statistical version of contact CR-product for Sasakian statistical manifolds.
Random Matrix Theory explains loss surface Hessians in neural networks.
problem Understanding the loss surfaces of neural networks.
method Investigation of local spectral statistics of neural network Hessians.
result Excellent agreement with Gaussian Orthogonal Ensemble statistics.
Paper develops a distributed debiased estimator for sparse statistical inference.
problem High computational costs in debiased estimator construction for high-dimensional models.
method Develops a multi-round distributed debiased estimator using both labeled and unlabelled data.
result Unlabeled data improves statistical rate of each iteration in distributed setup.
The paper advances U-statistics in dependent settings, improving spectral estimation and goodness-of-fit tests.
problem Non-asymptotic analysis of U-statistics in dependent Markov chain settings.
method Proved new concentration and exponential inequalities for U-statistics, applied to spectral estimation, online algorithms, and goodness-of-fit tests.
result Established new results for spectral estimation, online algorithms, and goodness-of-fit tests in Markov chain settings.
In recent publications, the authors have considered inverse statistics of the Dow Jones Industrial Averaged (DJIA) [1-3]. Specifically, we argued that the natural candidate for such statistics is the investment horizons distribution. This is the distribution of waiting times needed to achieve a predefined level of retu…
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
problem Exploring lightlike hypersurfaces and their properties in indefinite Sasakian statistical manifolds.
method Introducing indefinite Sasakian statistical manifolds and analyzing lightlike hypersurfaces with respect to dual connections.
result An invariant lightlike submanifold of an indefinite Sasakian statistical manifold is itself an indefinite Sasakian statistical manifold.