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Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
This paper presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the…
The performance of machine learning classification algorithms are evaluated by estimating metrics, often from the confusion matrix, using training data and cross-validation. However, these do not prove that the best possible performance has…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Estimating conditional average dose responses (CADR) is an important but challenging problem. Estimators must correctly model the potentially complex relationships between covariates, interventions, doses, and outcomes. In recent years, the…
Probabilities of causation (PoCs), such as the probability of necessity and sufficiency (PNS), are important tools for decision making but are generally not point identifiable. Existing work has derived bounds for these quantities using…
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…
We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
This survey paper focuses on the estimation schemes in molecular communication (MC) systems. The existing studies in estimation schemes can be divided into parameter estimation (e.g., distance, diffusion coefficient, and flow velocity) and…
In regression modelling approach, the main step is to fit the regression line as close as possible to the target variable. In this process most algorithms try to fit all of the data in a single line and hence fitting all parts of target…
We develop diffusion models for time-varying correlation using stochastic processes defined on the unit circle. Specifically, we study Brownian motion on the circle and the von Mises diffusion, and propose their use as continuous-time…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common…
Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…