arXiv research

Neural Empirical Bayes estimates source distributions from noisy simulations.

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…

Empirical Bayes rates via variational approximations and prior decomposition.

Personal income distributions in Japan are analyzed empirically and a simple stochastic model of the income process is proposed. Based on empirical facts, we propose a minimal two-factor model. Our model of personal income consists of an asset accumulation process and a wage process. We show that these simple processes…

Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.

Exact distribution of split conformal prediction coverage found.

We study 'meta-dependence' in conditional independence tests across different empirical distributions.

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…

Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.

We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well ap…

ECOD detects outliers without parameters, fast and simple.

We consider a financial market model which consists of a financial asset and a large number of interacting agents classified into many types. Different types of agents are heterogeneous in their price expectations. Each agent can change its type based on the current empirical distribution of the types and the equilibri…

We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these dis…

The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly "amplify" the effective amount of data available. For a large variety of distri…

Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.

We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected var…

This work studies the smooth 1-Wasserstein distance and its limit distribution in high dimensions.

A new framework tightens risk measure confidence 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…

The paper improves generative models to avoid replicating observed examples.

The hidden tail of empirical distributions is analyzed using extreme value theory.

New approach avoids excess empirical risk in domain generalization.

Improved eigenvalue distribution method for financial data.

Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.

Develops a robust learning method for unknown context distributions.

New algorithm optimizes unimodal bandits using empirical divergence.

This paper analyzes quantiles of heavy-tailed distributions, separating projection direction and quantile threshold effects.

Pareto's 80/20 rule follows a Gaussian distribution with twice the mean standard deviation.

Develops robust MDPs for unknown disturbances with performance guarantees.

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log…

Non-parametric time series forecasting without assuming a specific distribution.

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…

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 …

Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization will exactly recover the low rank matrix. In this article, we…

This study examines biases in flow matching samplers using finite-sample estimation.

Study analyzes stock market correlations using multivariate distributions.

Improved ADMM for convex distributed learning with differential privacy.

Transformers can learn Markov processes with constant depth, surprising results.

Auto-decoder synthesizes graphs from latent codes.

cCorrGAN approximates conditional correlation matrices using GANs.

Transformer pretraining yields strong EB performance without explicit adaptation.

Law derived for neural networks with sparse connections.

Unsupervised domain adaptation is a promising way to generalize deep models to novel domains. However, the current literature assumes that the label distribution is domain-invariant and only aligns the feature distributions or vice versa. In this work, we explore the more realistic task of Class-imbalanced Domain Adapt…

We study the risk performance of distributed learning for the regularization empirical risk minimization with fast convergence rate, substantially improving the error analysis of the existing divide-and-conquer based distributed learning. An interesting theoretical finding is that the larger the diversity of each local…

New statistical test for change-point detection using relative entropy.

EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.

Adaptive model learns from time series data with changing distributions.

The paper improves the empirical bootstrap method for non-normal estimators.