Related papers: An Improved Query for the Hidden Subgroup Problem
We study a basic problem of approximating the size of an unknown set $S$ in a known universe $U$. We consider two versions of the problem. In both versions the algorithm can specify subsets $T\subseteq U$. In the first version, which we…
It is widely believed that the backpropagation algorithm is essential for learning good feature detectors in early layers of artificial neural networks, so that these detectors are useful for the task performed by the higher layers of that…
Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…
We propose a generalization of Zhandry's compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability…
We present a lightweight approach to sequence classification using Ensemble Methods for Hidden Markov Models (HMMs). HMMs offer significant advantages in scenarios with imbalanced or smaller datasets due to their simplicity,…
Ashtiani et al. proposed a Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to make adaptive queries to a domain expert. The queries are of the kind "do two given points belong to the same optimal cluster?"…
Latent class models are widely used for identifying unobserved subgroups from multivariate categorical data in social sciences, with binary data as a particularly popular example. However, accurately recovering individual latent class…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…
Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…
Secret sharing in user hierarchy represents a challenging area for research. Although a lot of work has already been done in this direc- tion, this paper presents a novel approach to share a secret among a hierarchy of users while…
We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros…
Weakly supervised semantic segmentation is typically inspired by class activation maps, which serve as pseudo masks with class-discriminative regions highlighted. Although tremendous efforts have been made to recall precise and complete…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
If all of the entries of a large $S_n$ character table are covered up and you are allowed to uncover one entry at a time, then how can you quickly identify all of the indexing characters and conjugacy classes? We present a fast algorithmic…
We consider the basic problem of querying an expert oracle for labeling a dataset in machine learning. This is typically an expensive and time consuming process and therefore, we seek ways to do so efficiently. The conventional approach…