Related papers: Bucketing Coding and Information Theory for the St…
We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…
Proving capacity for networks without feedback or cooperation usually involves two fundamental random coding techniques: superposition coding and binning. Although conceptually very different, these two techniques often achieve the same…
The structure of data organization is widely recognized as having a substantial influence on the efficacy of machine learning algorithms, particularly in binary classification tasks. Our research provides a theoretical framework suggesting…
Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases,…
Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective…
In this work, binary block-to-block distribution matching is considered. m independent and uniformly distributed bits are mapped to n output bits resembling a target product distribution. A rate R is called achieved by a sequence of…
We consider algorithms to schedule packets with values and deadlines in a size-bounded buffer. At any time, the buffer can store at most B packets. Packets arrive over time. Each packet has a non-negative value and an integer deadline. In…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
Evaluation of link prediction methods is a hard task in very large complex networks because of the inhibitive computational cost. By setting a lower bound of the number of common neighbors (CN), we propose a new framework to efficiently and…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
We consider an approximation scheme for multivariate information assuming that synergistic information only appearing in higher order joint distributions is suppressed, which may hold in large classes of systems. Our approximation scheme…
We call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…
We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
This paper describes a search algorithm to find multiple sets of one dimensional unipolar (optical) orthogonal codes characterized by parameters, binary code sequence of length (n bits) and weight w (number of bit 1s in the sequence) as…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…