arXiv research

Graphical lasso may fail to fit models when data points are insufficient.

Paper uses SDP for community detection with side information.

Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined and it is shown that symmetric intervals are the shortest. The length of the sho…

Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A report…

Unified plug-in approach for estimating symmetric properties of distributions efficiently.

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

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex optimization formulation with a cost function consisting of the sum of a likeliho…

Study exact community detection in k-community Gaussian mixtures with different intensities.

Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known EM algorithm, their application to high-dimensional problems is still therefore c…

Study of Langevin dynamics for tensor PCA recovery in high dimensions.

This paper resolves the all-or-nothing phase transition in graph matching.

Exact recovery method for community detection in Gaussian mixtures with dependent noise.

Development of stock networks is an important approach to explore the relationship between different stocks in the era of big-data. Although a number of methods have been designed to construct the stock correlation networks, it is still a challenge to balance the selection of prominent correlations and connectivity of …

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A recent line of results showed--under mild assumptions--that the graphical lasso esti…

Likelihood from a generative model is a natural statistic for detecting out-of-distribution (OoD) samples. However, generative models have been shown to assign higher likelihood to OoD samples compared to ones from the training distribution, preventing simple threshold-based detection rules. We demonstrate that OoD det…

The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across clusters. In the asymptotic regime of $p=a \log n/n$ and $q=b \log n/n$ for fixe…

Estimates natural parameters of p-tensor Ising models efficiently.

Study connects database alignment and planted matching using Gaussian features.

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse u…

Proposes a conservative LR estimator for infrequent data near a frequency threshold.

A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and the latent conditional expectile. Nonlinear threshold specification is further i…

Maximum likelihood estimation fails to be well-posed in Gaussian process regression.

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explici…

Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community structure under the binary stochastic block model of two equal-sized clusters. The s…

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conserva…

Maximum likelihood training improves the performance of score-based diffusion models.

Study reconstructs hidden perfect matchings in random graphs with specific edge weights.

Corrects pseudo log-likelihood method issues in various applications.

Polynomial neural networks explore thresholds for maximum expressiveness.

We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. When the data is sparse, there are many zeros in the contingency table and the maximum likelihood estimate of th…

A new method speeds up quantum state estimation.

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure t…

Proposes a new approach to approximate maximum likelihood for complex models.

This paper improves normalizing flows by combining MLE and sliced-Wasserstein distance for better data fidelity.

Machine learning should incorporate maximum likelihood for better estimation.

We study the inference of a model of dynamic networks in which both communities and links keep memory of previous network states. By considering maximum likelihood inference from single snapshot observations of the network, we show that link persistence makes the inference of communities harder, decreasing the detectab…

Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.

We propose a robust estimator to improve maximum likelihood in probabilistic models.

Geometric approach solves maximum likelihood for Cauchy-like distributions.

New particle algorithms optimize latent variable models.

This work investigates training infinite mixtures with maximum likelihood for improved uncertainty quantification.

New method estimates latent gene expression factors without overlap with known confounders.

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

This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.

Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log marginal likelihood, which can be applied to both regular and singular models. When the…

Paper quantifies label shift robustly.

Paper presents a method for estimating Hawkes process parameters.

Geodesic descent optimizes likelihood in dually flat spaces.