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Pool of knowledge available to the mankind depends on the source of learning resources, which can vary from ancient printed documents to present electronic material. The rapid conversion of material available in traditional libraries to…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad…
Localizing text in low-light environments is challenging due to visual degradations. Although a straightforward solution involves a two-stage pipeline with low-light image enhancement (LLE) as the initial step followed by detector, LLE is…
Interpretable text representations should expose coordinates that are not only predictive, but also meaningful enough for independent auditors to apply. Existing discriminative representations often use anonymous embedding directions, while…
We present a method for the classification of multi-labelled text documents explicitly designed for data stream applications that require to process a virtually infinite sequence of data using constant memory and constant processing time.…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
We consider the 2-dimensional random matching problem in $\mathbb{R}^2.$ In a challenging paper, Caracciolo et. al. arXiv:1402.6993 on the basis of a subtle linearization of the Monge Ampere equation, conjectured that the expected value of…
Query term matching with document term matching is the basic function of any best effort Information Retrieval models like Vector Space Model. In our problem of SMS based Information Systems we expect common people to participate in…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Stereo vision generally involves the computation of pixel correspondences and estimation of disparities between rectified image pairs. In many applications, including simultaneous localization and mapping (SLAM) and 3D object detection, the…
The Hausdorff distance is a metric commonly used to compute the set similarity of geometric sets. For sets containing a total of $n$ points, the exact distance can be computed na\"{i}vely in $O(n^2)$ time. In this paper, we show how to…
Trace reconstruction considers the task of recovering an unknown string $x \in \{0,1\}^n$ given a number of independent "traces", i.e., subsequences of $x$ obtained by randomly and independently deleting every symbol of $x$ with some…
Given a pair of strings, the problems of computing their Longest Common Subsequence and Edit Distance have been extensively studied for decades. For exact algorithms, LCS and Edit Distance (with character insertions and deletions) are…
We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor; specifically, for strings of length n and every fixed epsilon>0, it can compute a (log n)^O(1/epsilon)…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
String Edit Distance is a more-than-classical problem whose behavior in the dynamic setting, where the strings are updated over time, is well studied. A single-character substitution, insertion, or deletion can be processed in time…
Outlier detection is a well-researched and crucial problem in machine learning. However, there is little research on string data outlier detection, as most literature focuses on outlier detection of numerical data. A robust string data…
Text detection in natural images is a challenging but necessary task for many applications. Existing approaches utilize large deep convolutional neural networks making it difficult to use them in real-world tasks. We propose a small yet…