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The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
In this paper, we present the Bennett-type generalization bounds of the learning process for i.i.d. samples, and then show that the generalization bounds have a faster rate of convergence than the traditional results. In particular, we…
In a 1976 paper published in Science, Knuth presented an algorithm to sample (non-uniform) self-avoiding walks crossing a square of side k. From this sample, he constructed an estimator for the number of such walks. The quality of this…
We present convergence results for an adaptive algorithm to compute free energies, namely the adaptive biasing force (ABF) method. The free energy is the effective potential associated to a so-called reaction coordinate (RC). Computing free…
The Newton method is a powerful optimization algorithm, valued for its rapid local convergence and elegant geometric properties. However, its theoretical guarantees are usually limited to convex problems. In this work, we ask whether…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine…
A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…
Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission…
Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g. large molecules or spin glasses. In simulations this usually…
We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An…
In property and casualty insurance, particularly in automobile insurance, risk exposure is commonly assumed to be proportional to the duration of coverage. This assumption leads to two standard estimation strategies: the ratio approach,…
We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic…
We propose a likelihood ratio statistic for forming hypothesis tests and confidence intervals for a nonparametrically estimated univariate regression function, based on the shape restriction of concavity (alternatively, convexity). Dealing…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such…