arXiv research

Dimensionality reduction methods are very common in the field of high dimensional data analysis. Typically, algorithms for dimensionality reduction are computationally expensive. Therefore, their applications for the analysis of massive amounts of data are impractical. For example, repeated computations due to accumula…

Kan extensions help in data science extrapolation and learning.

Let $X=\mathbf{X}\cup\mathbf{Z}$ be a data set in $\mathbb{R}^D$, where $\mathbf{X}$ is the training set and $\mathbf{Z}$ is the test one. Many unsupervised learning algorithms based on kernel methods have been developed to provide dimensionality reduction (DR) embedding for a given training set $Φ: \mathbf{X} \to \mat…

The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted…

This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends t…

New insights into identifying mixtures of product distributions using Hadamard extensions.

Many of the algorithms used to solve minimization problems with sparsity-inducing regularizers are generic in the sense that they do not take into account the sparsity of the solution in any particular way. However, algorithms known as semismooth Newton are able to take advantage of this sparsity to accelerate their co…

Responds to comments on Bayesian Logic Regression algorithm, provides extensions and tutorial.

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…

Recent student knowledge modeling algorithms such as Deep Knowledge Tracing (DKT) and Dynamic Key-Value Memory Networks (DKVMN) have been shown to produce accurate predictions of problem correctness within the same learning system. However, these algorithms do not attempt to directly infer student knowledge. In this pa…

Algorithm distinguishes Fuchsian groups with finite quotients.

Recent work has extended the theoretical analysis of boosting algorithms to multiclass problems and to online settings. However, the multiclass extension is in the batch setting and the online extensions only consider binary classification. We fill this gap in the literature by defining, and justifying, a weak learning…

Examines algorithmic modeling across three cultures.

The Gumbel-max trick and its extensions simplify sampling from categorical distributions in machine learning.

Paper addresses inefficiency in converting EFGs to NFGs for learning.

Instability and variability of Deep Reinforcement Learning (DRL) algorithms tend to adversely affect their performance. Averaged-DQN is a simple extension to the DQN algorithm, based on averaging previously learned Q-values estimates, which leads to a more stable training procedure and improved performance by reducing …

We present a method to extract a weighted finite automaton (WFA) from a recurrent neural network (RNN). Our algorithm is based on the WFA learning algorithm by Balle and Mohri, which is in turn an extension of Angluin's classic \lstar algorithm. Our technical novelty is in the use of \emph{regression} methods for the s…

Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to e…

New algorithm detects outliers from rare abnormal data.

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using this interpretation and techniques borrowed from convex optimization, we give a …

Training neural networks on image datasets generally require extensive experimentation to find the optimal learning rate regime. Especially, for the cases of adversarial training or for training a newly synthesized model, one would not know the best learning rate regime beforehand. We propose an automated algorithm for…

NP-iMCMC algorithm for nonparametric models in universal PPLs.

A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension …

This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including Gradient Descent, L-BFGS, Stochastic Gradient Descent, Conjugate Gradient, etc.), …

Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…

Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends …

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Ou…

Algorithm adapts to non-stationary rewards without prior knowledge.

Labeled Latent Dirichlet Allocation (LLDA) is an extension of the standard unsupervised Latent Dirichlet Allocation (LDA) algorithm, to address multi-label learning tasks. Previous work has shown it to perform in par with other state-of-the-art multi-label methods. Nonetheless, with increasing label sets sizes LLDA enc…

Modified K-means ensures local optimality with same complexity.

Extensions to given-data Sobol' index estimators for large models.

A fast spectral algorithm detects community structure in evolving graphs.

Benchmark assesses fairness in algorithmic uncertainty, revealing consistent and calibrated estimates improve fairness.

Proposes an EM algorithm for high-dimensional Markov-switching VAR models.

UTE improves reinforcement learning by measuring action uncertainty, enhancing policy learning efficiency.

In the era of big data, an important weapon in a machine learning researcher's arsenal is a scalable Support Vector Machine (SVM) algorithm. SVMs are extensively used for solving classification problems. Traditional algorithms for learning SVMs often scale super linearly with training set size which becomes infeasible …

Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended by Pham and Venkatesh to cope with the case where corruption to the CS data is modeled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS…

The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess ranking and multiclass classification. Numerous extensions of the basic model have a…

Cost-Sensitive Online Classification has drawn extensive attention in recent years, where the main approach is to directly online optimize two well-known cost-sensitive metrics: (i) weighted sum of sensitivity and specificity; (ii) weighted misclassification cost. However, previous existing methods only considered firs…

MARCO-GE selects clustering algorithms using graph embeddings.

Generalized Linear Bandits (GLBs), a natural extension of the stochastic linear bandits, has been popular and successful in recent years. However, existing GLBs scale poorly with the number of rounds and the number of arms, limiting their utility in practice. This paper proposes new, scalable solutions to the GLB probl…

Coagent policy gradient algorithms (CPGAs) are reinforcement learning algorithms for training a class of stochastic neural networks called coagent networks. In this work, we prove that CPGAs converge to locally optimal policies. Additionally, we extend prior theory to encompass asynchronous and recurrent coagent networ…

We introduce a framework for performing regression between two Hilbert spaces. This is done based on Kirszbraun's extension theorem, to the best of our knowledge, the first application of this technique to supervised learning. We analyze the statistical and computational aspects of this method. We decompose this task i…

XGBoost is often presented as the algorithm that wins every ML competition. Surprisingly, this is true even though predictions are piecewise constant. This might be justified in high dimensional input spaces, but when the number of features is low, a piecewise linear model is likely to perform better. XGBoost was exten…

An important preprocessing step in most data analysis pipelines aims to extract a small set of sources that explain most of the data. Currently used algorithms for blind source separation (BSS), however, often fail to extract the desired sources and need extensive cross-validation. In contrast, their rarely used probab…

Paper extends Chernoff sampling for active testing and parameter estimation, improving neural network and regression models.

Fair HAC algorithms ensure clustering fairness across protected groups.

In this paper, we address the problem of reconstructing coverage maps from path-loss measurements in cellular networks. We propose and evaluate two kernel-based adaptive online algorithms as an alternative to typical offline methods. The proposed algorithms are application-tailored extensions of powerful iterative meth…