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Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of…
For a given dataset $\mathcal{D}$ and structured label $f$, the goal of Filtered Approximate Nearest Neighbor Search (FANNS) algorithms is to find top-$k$ points closest to a query that satisfy label constraints, while ensuring both recall…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…
Approximate nearest neighbor search (ANNS) constitutes an important operation in a multitude of applications, including recommendation systems, information retrieval, and pattern recognition. In the past decade, graph-based ANNS algorithms…
Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks. Recent work in the field of model compression studied binarized neural…
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts,…
Running complex sets of machine learning experiments is challenging and time-consuming due to the lack of a unified framework. This leaves researchers forced to spend time implementing necessary features such as parallelization, caching,…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive…
Network alignment (NA) aims to identify node correspondence across different networks and serves as a critical cornerstone behind various downstream multi-network learning tasks. Despite growing research in NA, there lacks a comprehensive…
We develop R2N, a modified quasi-Newton method for minimizing the sum of a $\mathcal{C}^1$ function $f$ and a lower semi-continuous prox-bounded $h$. Both $f$ and $h$ may be nonconvex. At each iteration, our method computes a step by…
Model merging has gained prominence in machine learning as a method to integrate multiple trained models into a single model without accessing the original training data. While existing approaches have demonstrated success in domains such…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
In this study, a new Stacked Generalization technique called Fuzzy Stacked Generalization (FSG) is proposed to minimize the difference between N -sample and large-sample classification error of the Nearest Neighbor classifier. The proposed…