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Measurement update rules for Bayes filters often contain hand-crafted heuristics to compute observation probabilities for high-dimensional sensor data, like images. In this work, we propose the novel approach Deep Measurement Update (DMU)…
An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space…
This paper introduces Monotone Delta, an order-theoretic measure designed to enhance the reliability assessment of survey-based instruments in human-machine interactions. Traditional reliability measures, such as Cronbach's Alpha and…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
Fairness is a principal social value that can be observed in civilisations around the world. A manifestation of this is in social agreements, often described in texts, such as contracts. Yet, despite the prevalence of such, a fairness…
Establishing the frequentist properties of Bayesian approaches widens their appeal and offers new understanding. In hypothesis testing, Bayesian model averaging addresses the problem that conclusions are sensitive to variable selection. But…
The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit…
The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work…
Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However,…
Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
The main purpose is to show that Feigenbaum delta constant is much more universal than believed. The paper is mainly devoted to period-doubling processes in families in one parameter of endomorphisms of the interval and consider…
Angluin's L$^*$ algorithm learns the minimal deterministic finite automaton (DFA) of a regular language using membership and equivalence queries. Its probabilistic approximatively correct (PAC) version substitutes an equivalence query by…
Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical value of parameters the equilibrium with two pairs of double…
Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some…
We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…
We review current methods for building PSF-matching kernels for the purposes of image subtraction or coaddition. Such methods use a linear decomposition of the kernel on a series of basis functions. The correct choice of these basis…