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This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
The widespread use and popularity of collaborative content sites (e.g., IMDB, Amazon, Yelp, etc.) has created rich resources for users to consult in order to make purchasing decisions on various products such as movies, e-commerce products,…
Maximum Inner Product Search (MIPS) is a fundamental challenge in machine learning and information retrieval, particularly in high-dimensional data applications. Existing approaches to MIPS either rely solely on Inner Product (IP)…
We revisit the problem of large-scale assortment optimization under the multinomial logit choice model without any assumptions on the structure of the feasible assortments. Scalable real-time assortment optimization has become essential in…
We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…
Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…
We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization…
The goal of diversity sampling is to select a representative subset of data in a way that maximizes information contained in the subset while keeping its cardinality small. We introduce the ordered diverse sampling problem based on a new…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
From a process development perspective, diamond growth via chemical vapor deposition has made significant strides. However, challenges persist in achieving high quality and large-area material production. These difficulties include…
Exact Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Due to the wide applications in recommendation systems, multi-class label prediction and deep learning, the Maximum Inner Product (MIP) search problem has received extensive attention in recent years. Faced with large-scale datasets…
We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from $\{0,1\}$ or $\{-1,1\}$. We describe efficient parallel algorithms for…
Importance sampling and independent Metropolis-Hastings (IMH) are among the fundamental building blocks of Monte Carlo methods. Both require a proposal distribution that globally approximates the target distribution. The Radon-Nikodym…
After initial proof-of-principle demonstrations, optically pumped nitrogen-vacancy (NV) centres in diamond have been proposed as a non-invasive platform to achieve hyperpolarisation of nuclear spins in molecular samples over macroscopic…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…