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The aim of this paper is to describe new statistical methods for determination of the correlations among and distributions of physical parameters from a multivariate data with general and arbitrary truncations and selection biases. These…
We introduce a differentially private method to measure nonlinear correlations between sensitive data hosted across two entities. We provide utility guarantees of our private estimator. Ours is the first such private estimator of nonlinear…
Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors we show that the…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause…
The proposal of Reshef et al. (2011) is an interesting new approach for discovering non-linear dependencies among pairs of measurements in exploratory data mining. However, it has a potentially serious drawback. The authors laud the fact…
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We…
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…
Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training…
Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some…
Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…
This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance…
We present an improvement of the phase distance correlation (PDC) periodogram to account for uncertainties in the time-series data. The PDC periodogram introduced in our previous papers is based on the statistical concept of distance…
Quantum correlations often defy an explanation in terms of fundamental notions of classical physics, such as causality, locality, and realism. While the mathematical theory underpinning quantum correlations between spacelike separated…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. This work focuses on estimating the causal effect between two time series that are confounded by a third, unobserved time…