arXiv research

Develops robust MDPs for unknown disturbances with performance guarantees.

We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…

This paper studies convergence properties of multivariate distributions constructed by endowing empirical margins with a copula. This setting includes Latin Hypercube Sampling with dependence, also known as the Iman--Conover method. The primary question addressed here is the convergence of the component sum, which is r…

New method corrects bias in datasets using cumulative distribution functions.

Neural Empirical Bayes estimates source distributions from noisy simulations.

Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.

Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…

Estimates score function from data with optimal rate in high dimensions.

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework exte…

WES improves neural network regression by stretching distribution error.

Paper identifies unobserved variables from observable data.

A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency …

The paper studies empirical processes from nearest neighbors in regression.

PVI improves SIVI by directly optimizing ELBO without parametric assumptions.

Distributional reinforcement learning (distributional RL) has seen empirical success in complex Markov Decision Processes (MDPs) in the setting of nonlinear function approximation. However, there are many different ways in which one can leverage the distributional approach to reinforcement learning. In this paper, we p…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization term…

Changes (returns) in stock index prices and exchange rates for currencies are argued, based on empirical data, to obey a stable distribution with characteristic exponent $α< 2$ for short sampling intervals and a Gaussian distribution for long sampling intervals. In order to explain this phenomenon, an Ehrenfest model…

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…

A new method uses normalizing flows to approximate optimal transport between empirical distributions.

New metrics avoid high-dimensional analysis challenges, proving convergence without 'curse of dimensionality'.

We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a $k$-dimensional subspace. We show that this task is connected with another classical prob…

New learning algorithm for real analytic functions without gradient descent.

ECOD detects outliers without parameters, fast and simple.

The paper bounds the expectation of empirical processes indexed by Hölder classes.

Corrects sample selection bias in empirical risk minimization using importance sampling.

Distributed machine learning is an approach allowing different parties to learn a model over all data sets without disclosing their own data. In this paper, we propose a weighted distributed differential privacy (WD-DP) empirical risk minimization (ERM) method to train a model in distributed setting, considering differ…

Optimal score function estimation via empirical risk minimization

Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.

Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's law in the high region and the non-Gibrat's law in the middle region, we kinematically derive the profits distribution funct…

The paper examines the tilted empirical risk's generalization and robustness under negative tilt.

The paper introduces a DRM for causal inference, offering a flexible method to analyze counterfactual distributions.

New margin-based learning guarantees improve generalization bounds.

Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $τ(β)$. Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is…

Decentralized learning for GLMs with feature distribution and network connectivity.

Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to scale. These extensions are needed in order to explain the regularities of the empiri…

The study bounds the utility of empirically optimal portfolios using stock return data.

Study analyzes stock market correlations using multivariate distributions.

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses smoothed empirical characteristic functions to represent the distributions, the s…

In the spirit of the emergent field of econophysics, a goodness-of-fit test for the Power-Law distribution, based on the Empirical Distribution Function (EDF) is presented, and related problems are discussed. An analysis of the tail behaviour of the daily logarithmic variation of the Mexican Stock Market Index (IPC), s…

The paper proposes a new method for density estimation using spline quasi-interpolation for clustering.

Improved ADMM for convex distributed learning with differential privacy.

Neural networks estimate statistical divergences with performance guarantees.

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence…

Uniform consistency proven for spatial distribution and depth estimators in any dimension.

We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-…

In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails,…

Bayesian networks with latent variables are characterized and their likelihoods compared.

Researchers define quantiles on Riemannian manifolds using optimal transport.