Related papers: An optimality property of the Bayes-Kelly algorith…
We study a simple model of unsupervised learning where the single symmetry breaking vector has binary components $\pm 1$. We calculate exactly the Bayes-optimal performance of an estimator which is required to lie in the same discrete…
The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…
We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
It is pointed out that a loophole exists in experimental tests of Bell inequality using atomic qubits, due to possible errors in the rotation angles of the atomic states. A sufficient condition is derived for closing the loophole.
In a previous paper, published in 1992, a primal conical LP algorithm with exact finite coonvergence was presented. The underlying optimality condition requires tangency of two sets (an affine space and a cone). In the algorithm the two…
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all…
Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present…
We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the…
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model.…
In this paper, we consider a simple discrete-time optimal betting problem using the celebrated Kelly criterion, which calls for maximization of the expected logarithmic growth of wealth. While the classical Kelly betting problem can be…