A universal method for hypothesis tests and confidence sets without regularity conditions.
problem Difficult inference in irregular statistical models.
method Modified likelihood ratio statistic (split LRT).
result Works for any parametric and some nonparametric models.
A novel kernel-based test detects equality versus singularity of two probability measures.
problem Detecting equality versus singularity of two probability distributions.
method Combines kernel mean and kernel covariance embeddings to construct a likelihood ratio test statistic.
result The test statistic satisfies a '0/\infty' law, vanishing under the null and diverging under the alternative.
Neural networks approximate likelihood ratios for complex models.
problem Difficulty in computing likelihood ratios for modern models.
method Applying the likelihood ratio trick with neural network classifiers.
result Different neural network setups can approximate likelihood ratios with varying performance.
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.
problem Enhancing predictive model reliability by allowing uncertain predictions.
method Neyman--Pearson lemma applied to likelihood ratios for optimal selection.
result Neyman--Pearson-informed methods outperform existing baselines under covariate shifts.
A new algorithm detects changes in data with constant cost per iteration.
problem Detecting changes in data with low computational cost.
method Adapting pruning and maximisation techniques from Gaussian data to exponential family models.
result The algorithm can detect changes in a wide range of models with a constant per-iteration cost.
A test for neural networks identifies genetic associations.
problem Testing complex associations in neural networks.
method Sieve quasi-likelihood ratio test for neural networks with one hidden layer.
result The test statistic has an asymptotic chi-squared distribution.
Extends likelihood ratio exponential families to analyze various optimization methods.
problem Analyzing optimization methods like rate-distortion and information bottleneck.
method Linking geometric mixture paths to exponential families and using hypothesis testing.
result Provides a common mathematical framework for understanding these methods.
Efficient tests achieve best error rates in high-dimensional hypothesis testing.
problem Achieving optimal error rates in computationally efficient hypothesis testing.
method Linear spectral statistics and low-degree likelihood ratio analysis.
result An efficient test achieves the best possible error rates among all computationally efficient tests.
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…
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…
The paper analyzes a private likelihood-ratio test for frequency tables under differential privacy constraints.
problem Achieving privacy in statistical data analysis while maintaining statistical utility.
method A rigorous analysis of a private likelihood-ratio (LR) test for goodness-of-fit in frequency tables, considering (ε,δ)-differential privacy. result Characterization of the trade-off between differential privacy parameters (ε,δ) and statistical power of the private LR test. Near-optimal private tests for simple and MLR hypotheses developed under Gaussian differential privacy.
problem Developing private tests for simple and MLR hypotheses under Gaussian differential privacy.
method A private mean estimator with data-driven clamping bounds, constructing private test statistics.
result Private tests achieve the same asymptotic relative efficiency as non-private most powerful tests.
FF algorithm uses goodness as a likelihood-ratio test for scalar normalization.
problem Training each layer locally with scalar goodness.
method FF algorithm uses a likelihood-ratio test with squared goodness as the sufficient statistic.
result The FF algorithm generalizes to anisotropic and heavy-tailed populations.
FF algorithm uses goodness as a measure of input quality, derived from likelihood-ratio tests.
problem Training each layer locally with a goodness measure.
method FF algorithm uses a likelihood-ratio test to define goodness, which is the sum of squared activations normalized between layers.
result The goodness measure is a sufficient statistic for a likelihood-ratio test, explaining the FF algorithm's performance.
Develops neural network methods for likelihood ratio estimation.
problem Estimating likelihood ratios from data.
method Neural network training for likelihood ratio estimation.
result Unified methodology for defining and solving optimization problems.
Proposes a test for stochastic block models with bounded degrees.
problem Testing Erdös-Rényi model versus bisection stochastic block model with bounded degrees.
method Likelihood-ratio (LR) type procedure based on regularization.
result Limit distributions as power Poisson laws under null and alternative hypotheses.
Study benchmarks TSC algorithms in distinguishing diffusions using the likelihood ratio test.
problem Benchmarking optimality of TSC algorithms in distinguishing diffusion processes.
method Proposes to benchmark TSC algorithms using the likelihood ratio test (LRT).
result LRT benchmarks are computationally efficient and can be applied to various time series types.
Develops GLRT for defending against adversarial attacks in hypothesis testing.
problem Adversarial attacks on machine learning models causing misclassification.
method Generalized likelihood ratio test applied to composite hypothesis testing problem.
result GLRT approach yields competitive robustness-accuracy tradeoff under various attacks.
Surveying a new method to predict computational hardness in hypothesis testing.
problem Understanding statistical-versus-computational tradeoffs in high-dimensional inference problems.
method The low-degree method, which predicts computational hardness using the second moment of the low-degree likelihood ratio.
result Sharp low-degree lower bounds against subexponential-time algorithms for tensor PCA.
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
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…
Optimal private tests for simple hypotheses are characterized.
problem Private testing of simple hypotheses under differential privacy constraints.
method Characterization of sample complexity and optimal tests using log-likelihood ratio tests.
result Optimal sample complexity achieved by a specific randomized and clamped variant of the log-likelihood ratio test.
This paper develops embeddings that preserve likelihood-based statistical inference.
problem Modern machine learning embeddings destroy the geometric structure required for likelihood-based inference.
method Developed a rigorous theory of likelihood-preserving embeddings and introduced the Likelihood-Ratio Distortion metric.
result Controlling the distortion Δn is necessary and sufficient for preserving inference. New optimization methods for neural networks improve classification accuracy.
problem Optimizing shallow networks for binary classification.
method Introducing a new family of optimization problems not covered by existing methods.
result New training algorithms with stable convergence and improved performance.
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…
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…
We estimate Radon-Nikodym derivatives using regularization in reproducing kernel Hilbert spaces.
problem Estimating Radon-Nikodym derivatives in various applications.
method General regularization scheme in reproducing kernel Hilbert spaces.
result High order accuracy in reconstructing Radon-Nikodym derivatives at any point.
New method detects changes in high-dimensional Gaussian data streams.
problem Detecting changes in high-dimensional data streams.
method Likelihood ratio tests across scales and coordinates.
result Patience (null rejection rate) at desired level, response delay under alternative.
SPRT-TANDEM improves sequential classification accuracy with fewer samples.
problem Efficiently classifying sequential data with high accuracy and low sampling cost.
method Deep neural network-based SPRT algorithm that estimates log-likelihood ratio of two hypotheses.
result SPRT-TANDEM achieves statistically significantly better classification accuracy than other classifiers with fewer samples.
Paper tackles informative labels in semi-supervised learning, proposing debiasing methods.
problem Informative labels can bias semi-supervised learning models, especially when some classes are more likely to be labeled.
method Estimates missing-data mechanism and uses inverse propensity weighting to debias SSL algorithms.
result Proposed methods improve SSL performance, demonstrated on various datasets including medical ones.
Revises precision-recall curves for generative models.
problem Improves evaluation of generative models by distinguishing mode-collapse and quality issues.
method Generalizes PR curve formulation to arbitrary measures, exposes a bridge to error rates, proposes a new algorithm to approximate precision-recall curves.
result Demonstrates the interest of the new formulation over the original approach on multi-modal datasets.
Locally Optimized Random Forests adapt to different data distributions.
problem Predicting at unlabeled points from a different distribution than training data.
method Combining random forests with weighted importance sampling based on likelihood ratio.
result Improves prediction accuracy for extreme events.
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…
Study shows how to reduce variational inference bias by concentrating likelihood ratio distribution.
problem Bias and variance issues in variational inference.
method Upper bound variational gap using dispersion measure of likelihood ratio, suggesting methods to reduce bias.
result Reducing bias in variational inference can be achieved by making likelihood ratio distribution more concentrated.
Study tests whether trade-off functions are above or below benchmarks using finite samples.
problem Testing trade-off functions between unknown distributions.
method Identifies a condition for nontrivial testing, constructs a test with error guarantees, and inverts the test for confidence bands.
result Finite-sample testing is possible under specific structural assumptions about rejection regions.
Paper tackles moment estimation under covariate shift with a two-stage algorithm.
problem Estimating moments under covariate shift when source and target distributions differ.
method Proposes a two-stage algorithm: first, an optimal estimator for the source distribution; second, likelihood ratio reweighting for calibration.
result Achieves minimax optimal bound for moment estimation.
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the χ2 test and the likelihood ratio test ca…
Novel neural likelihood ratio estimation for negative data in particle physics.
problem Estimating likelihood ratios with negative probability densities and weights.
method Introducing a novel loss function and a new model architecture based on signed mixture models.
result Demonstrated improved estimation on a real-world example from particle physics.
E-C2ST uses E-values for high-dimensional data two-sample tests.
problem Statistical testing for high-dimensional data.
method Combines split likelihood ratio tests and predictive independence tests, using E-values for anytime-valid sequential tests.
result E-C2ST achieves enhanced statistical power by partitioning datasets into multiple batches.
Paper detects changes in graph-based data streams using likelihood-ratios.
problem Detecting changes in synchronized graph-based data streams.
method Kernel-based likelihood-ratio estimation over graph nodes.
result Effective detection and localization of change-points.
WCPS extends CPS to handle covariate shifts, providing probabilistically calibrated predictions.
problem Applying CPS to scenarios with covariate shifts.
method WCPS uses likelihood ratios between training and testing covariate distributions.
result WCPS are probabilistically calibrated under covariate shift.
Estimates network causal effects considering contagion and latent confounding.
problem Determining if correlations in network studies are due to contagion or latent confounding.
method Segregated graph representation, likelihood ratio tests, network causal effect estimation strategies.
result Proposes methods to estimate network causal effects under full interference scenarios.
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 …
Improved online changepoint detection for autocorrelated data.
problem Changepoint detection in autocorrelated data with false positives or delays.
method Generalized Likelihood Ratio (GLR) statistic for AR(p) processes, online focus algorithm.
result AR(p)-focus algorithm achieves high detection power in correlated data.
Develops a new test for comparing two groups' densities, showing minimax optimality.
problem Comparing probability densities between two groups.
method Probabilistic tensor product smoothing spline framework for joint density modeling; penalized likelihood ratio test for interaction testing.
result Proposed test is minimax optimal and outperforms conventional approaches.
New method reduces errors in pricing and sensitivities for discontinuous payoffs.
problem Errors in pricing and sensitivities for discontinuous payoffs in digital and barrier options.
method Alternative methods for estimating sensitivities, including likelihood ratio and hybrid methods.
result New methods substantially reduce test errors in prices and sensitivities.
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to …