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A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
Robust training of machine learning models in the presence of outliers has garnered attention across various domains. The use of robust losses is a popular approach and is known to mitigate the impact of outliers. We bring to light two…
Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, the MPC has some significant challenges for such systems. Its high computational complexity results in high…
Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
A recent paper (Neural Networks, {\bf 132} (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its…
The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…
This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
We present an adaptive approach for robust learning from corrupted training sets. We identify corrupted and non-corrupted samples with latent Bernoulli variables and thus formulate the learning problem as maximization of the likelihood…
This paper concerns the distributed training of nonlinear kernel machines on Map-Reduce. We show that a re-formulation of Nystr\"om approximation based solution which is solved using gradient based techniques is well suited for this,…
It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
Model agnostic meta-learning (MAML) is a popular state-of-the-art meta-learning algorithm that provides good weight initialization of a model given a variety of learning tasks. The model initialized by provided weight can be fine-tuned to…
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space…