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Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system, are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which…
The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…
Transporting findings from a study population to a target population is central to evidence-based decision-making in real-world settings. Most existing methods require individual-level data from both populations to account for covariate…
Conjunction assessment requires knowledge of the uncertainty in the predicted orbit. Errors in the atmospheric density are a major source of error in the prediction of low Earth orbits. Therefore, accurate estimation of the density and…
This work presents a non-parametric spatio-temporal model for mapping human activity by mobile autonomous robots in a long-term context. Based on Variational Gaussian Process Regression, the model incorporates prior information of spatial…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We introduce and analyze a new Markov model of the IEEE 802.11 Distributed Coordination Function (DCF) for wireless networks. The new model is derived from a detailed DCF description where transition probabilities are determined by precise…
This paper presents a new multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a Euclidean ball with high probability. We develop a new formulation for ball-shaped ambiguity sets of Gaussian…
In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with…
The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…
When predicting trajectories of road agents, motion predictors usually approximate the future distribution by a limited number of samples. This constraint requires the predictors to generate samples that best support the task given task…