Related papers: On a Multiplicative Algorithm for Computing Bayesi…
We consider the question of the largest possible combinatorial diameter among $(d-1)$-dimensional simplicial complexes on $n$ vertices, denoted $H_s(n, d)$. Using a probabilistic construction we give a new lower bound on $H_s(n, d)$ that is…
DuMouchel and Jones (1994) proposed the Bayesian D criterion by modifying the D-optimality approach to reduce dependence of the selected design on an assumed model. This criterion has been applied to select various single-stratum designs…
A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the…
Distributed and iterative network utility maximization algorithms, such as the primal-dual algorithms or the network-user decomposition algorithms, often involve trajectories where the iterates may be infeasible, convergence to the optimal…
Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient…
An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the "classical" case of…
We consider the problem of estimating the multiplicity of a polynomial when restricted to the smooth analytic trajectory of a (possibly singular) polynomial vector field at a given point or points, under an assumption known as the…
Algorithms for determining quality/cost/price tradeoffs in saturated markets are considered. A product is modeled by $d$ real-valued qualities whose sum determines the unit cost of producing the product. This leads to the following…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
We use the geometry of suitably generalised potentials to solve risk-sensitive Markovian optimal stopping problems. As in the linear case due to Dynkin and Yushkievich (1967), the value function is the pointwise infimum of those functions…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms…
In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…
Submodularity is one of the most important property of combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of $k$-submodular function is NP-hard, and approximation algorithms are studied. For…
The noisy-or and its generalization noisy-max have been utilized to reduce the complexity of knowledge acquisition. In this paper, we present a new representation of noisy-max that allows for efficient inference in general Bayesian…
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
The performance of many machine learning models depends on their hyper-parameter settings. Bayesian Optimization has become a successful tool for hyper-parameter optimization of machine learning algorithms, which aims to identify optimal…