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Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains…

Two of the principle tasks of causal inference are to define and estimate the effect of a treatment on an outcome of interest. Formally, such treatment effects are defined as a possibly functional summary of the data generating…

Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Empirical researchers increasingly use upstream machine-learning (ML) methods to construct proxies for latent target variables from complex, unstructured data. A naive plug-in use of such proxies in downstream econometric models, however,…

We consider the statistical analysis of heterogeneous data for prediction in situations where the observations include functions, typically time series. We extend the modeling with Mixtures-of-Experts (ME), as a framework of choice in…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a…

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this…

We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have…

Trial-based economic evaluations are typically performed on cross-sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and…

This paper studies the generalization of the targeted minimum loss-based estimation (TMLE) framework to estimation of effects of time-varying interventions in settings where both interventions, covariates, and outcome can happen at…

We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via…

We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with…

This paper introduces the minimum error entropy (MEE) criterion as an advanced information-theoretic loss function tailored for deep learning applications in wireless communications. The MEE criterion leverages higher-order statistical…

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…