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Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…

Any data annotation for subjective tasks shows potential variations between individuals. This is particularly true for annotations of emotional responses to musical stimuli. While older approaches to music emotion recognition systems…

We provide methods to validate and compare sensor outputs, or inference algorithms applied to sensor data, by adapting statistical scoring rules. The reported output should either be in the form of a prediction interval or of a parameter…

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…

Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two…

Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…

Data observed at high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or a smooth random function, and measurement error. Supposing…

We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically…

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…

In this paper, I proof that Importance Sampling estimates based on dependent sample sets are consistent under certain conditions. This can be used to reduce variance in Bayesian Models with factorizing likelihoods, using sample sets that…

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical…

In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…

As teamwork becomes ever-more important in a new age of remote work, it is critical to develop metrics to quantitatively evaluate how effective teams are. This is especially true with mixed-modality teams, such as those that include a human…

Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the…

Logarithmic score and information divergence appear in information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to regret…