Related papers: On the application of Good-Turing statistics to qu…
We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus far unobserved) biomolecular structures, and showed that the method is…
Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…
We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics,…
We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…
Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly…
Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
When studying high-dimensional dynamical systems such as macromolecules, quantum systems and polymers, a prime concern is the identification of the most probable states and their stationary probabilities or free energies. Often, these…
Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics,…
Large sample size equivalence between the celebrated {\it approximated} Good-Turing estimator of the probability to discover a species already observed a certain number of times (Good, 1953) and the modern Bayesian nonparametric counterpart…