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Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
To check the accuracy of Bayesian computations, it is common to use rank-based simulation-based calibration (SBC). However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is…
Benchmark experiments are required to test, compare, tune, and understand optimization algorithms. Ideally, benchmark problems closely reflect real-world problem behavior. Yet, real-world problems are not always readily available for…
We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…
The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…
Bayesian optimization (BO) is a widely-used sequential method for zeroth-order optimization of complex and expensive-to-compute black-box functions. The existing BO methods assume that the function evaluation (feedback) is available to the…
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…
We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradign for quantum tomography with attractive…
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
Bayesian Optimization is a popular approach for optimizing expensive black-box functions. Its key idea is to use a surrogate model to approximate the objective and, importantly, quantify the associated uncertainty that allows a sequential…
Simulation models, in particular agent-based models, are gaining popularity in economics. The considerable flexibility they offer, as well as their capacity to reproduce a variety of empirically observed behaviours of complex systems, give…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…