arXiv research

Neural networks approximate likelihood ratios for complex models.

A novel kernel-based test detects equality versus singularity of two probability measures.

We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a modified version of the usual likelihood ratio statistic, that we call "the split li…

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for k…

Optimal selective classification using likelihood ratios improves model reliability.

This paper develops embeddings that preserve likelihood-based statistical inference.

A density ratio is defined by the ratio of two probability densities. We study the inference problem of density ratios and apply a semi-parametric density-ratio estimator to the two-sample homogeneity test. In the proposed test procedure, the f-divergence between two probability densities is estimated using a density-r…

A new algorithm detects changes in data with constant cost per iteration.

Extends likelihood ratio exponential families to analyze various optimization methods.

A test for neural networks identifies genetic associations.

Efficient tests achieve best error rates in high-dimensional hypothesis testing.

Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribu…

FF algorithm uses goodness as a likelihood-ratio test for scalar normalization.

Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…

Study detects signals in spiked Wigner models using log likelihood ratio.

FF algorithm uses goodness as a measure of input quality, derived from likelihood-ratio tests.

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters $θ$ of an underlying theory and measurement apparatus to hig…

This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. S…

The paper analyzes a private likelihood-ratio test for frequency tables under differential privacy constraints.

Near-optimal private tests for simple and MLR hypotheses developed under Gaussian differential privacy.

Study benchmarks TSC algorithms in distinguishing diffusions using the likelihood ratio test.

Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family. In a data-driven version we replace this requirement with the availability of da…

SPRT-TANDEM improves sequential classification accuracy with fewer samples.

Develops GLRT for defending against adversarial attacks in hypothesis testing.

These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a certain quantity -- the second moment of the low-degree likelihood ratio -- gives…

Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one can still construct hypothesis tests and confidence sets with proper coverage and…

PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions un…

Direct neural ratio estimator for likelihood-free inference.

The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…

Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods …

We estimate Radon-Nikodym derivatives using regularization in reproducing kernel Hilbert spaces.

The paper studies inference in hypergraph β-models with multiple layers.

A method uses neural networks to approximate sampling distributions of test statistics.

A fundamental problem in network data analysis is to test Erdös-Rényi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are constants that represent the expected degrees of the graphs and $n$ denotes the number o…

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic n…

Novel neural likelihood ratio estimation for negative data in particle physics.

New method detects changes in high-dimensional Gaussian data streams.

Paper detects changes in graph-based data streams using likelihood-ratios.

Paper tackles informative labels in semi-supervised learning, proposing debiasing methods.

Proposes incorporating noise sources in machine learning evaluation for more reliable conclusions.

Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution …

We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does no…

Paper tackles moment estimation under covariate shift with a two-stage algorithm.

Model change points in time-series data with neural SDEs and variational autoencoders.

New algorithm for efficiently identifying the best arm in stochastic bandits.

The paper tackles hypothesis testing for likelihood-free inference with a new kernel-based approach.

This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Wi…

New machine learning methods for inference from simulated data.