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We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Cross-modal alignment is a crucial task in multimodal learning aimed at achieving semantic consistency between vision and language. This requires that image-text pairs exhibit similar semantics. Traditional algorithms pursue embedding…
This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Localizing a cloud of points from noisy measurements of a subset of pairwise distances has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. In [1], Drineas…
Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Criteria for scaling based on empirical acceptance rates of algorithms have been found to work consistently well across a broad range…
The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent…
Due to the outstanding capability of capturing underlying data distributions, deep learning techniques have been recently utilized for a series of traditional database problems. In this paper, we investigate the possibilities of utilizing…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
The failure of the Euclidean norm to reliably distinguish between nearby and distant points in high dimensional space is well-known. This phenomenon of distance concentration manifests in a variety of data distributions, with iid or…
Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a…
Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric…
Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…
The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance…
The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement,…