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We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces…
Parameters of sub-populations can be more relevant than super-population ones. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned…
Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…
Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
This paper discusses the application of L1-regularized maximum entropy modeling or SL1-Max [9] to multiclass categorization problems. A new modification to the SL1-Max fast sequential learning algorithm is proposed to handle conditional…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
We demonstrate the effectiveness of the categorical distribution as a neural network output for next event prediction. This is done for both discrete-time and continuous-time event sequences. To model continuous-time processes, the…
We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
We study the problem of maximizing R{\'e}nyi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…