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Given a huge, online stream of time-evolving events with multiple attributes, such as online shopping logs: (item, price, brand, time), and local mobility activities: (pick-up and drop-off locations, time), how can we summarize large,…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
We consider the frequency estimation of periodic signals using noisy time-of-arrival (TOA) information with missing (sparse) data contaminated with outliers. We tackle the problem from a mathematical optimization standpoint, formulating it…
When facing a very large stream of data, it is often desirable to extract most important statistics online in a short time and using small memory. For example, one may want to quickly find the most influential users generating posts online…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
We consider the problem of estimating the covariance matrix of a random signal observed through unknown translations (modeled by cyclic shifts) and corrupted by noise. Solving this problem allows to discover low-rank structures masked by…
This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…
The success of deep learning requires high-quality annotated and massive data. However, the size and the quality of a dataset are usually a trade-off in practice, as data collection and cleaning are expensive and time-consuming. In…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…
Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…
We consider a ranking problem where we have noisy observations from a matrix with isotonic columns whose rows have been permuted by some permutation $\pi$ *. This encompasses many models, including crowd-labeling and ranking in tournaments…
Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we…
Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and…
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
While anomaly detection in time series has been an active area of research for several years, most recent approaches employ an inadequate evaluation criterion leading to an inflated F1 score. We show that a rudimentary Random Guess method…
Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…