Related papers: An Efficient Reversible Algorithm for Linear Regre…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Regression is a cornerstone of statistics and machine learning, with applications spanning science, engineering, and economics. While quantum algorithms for regression have attracted considerable attention, most existing work has focused on…
We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…
We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used.…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
In the recent publication (arxiv:2007.08063v2 [cs.LG]) a fast prediction algorithm for a single recurrent network (RN) was suggested. In this manuscript we generalize this approach to a chain of RNs and show that it can be implemented in…
At a fundamental level most physical equations are time reversible. In this paper we propose an integrator that preserves this property at the discrete computational level. Our simulations can be run forward and backwards and trace the same…
Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…
Reversible algorithms are algorithms in which each step represents a partial injective function; they are useful for performance optimization in reversible systems. In this study, using Janus, a reversible imperative high-level programming…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
A fast Non-linear and non-iterative learning and classification algorithm is synthesized and validated. This algorithm named the "Reverse Ripple Effect(R.R.E)", achieves 100% learning accuracy but is computationally expensive upon…
We propose a natural intrinsic extension of ridge regression from Euclidean spaces to general Riemannian manifolds for time-series prediction. Our approach combines Riemannian least-squares fitting via B\'ezier curves, empirical covariance…
The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…
Algorithmic recourse provides individuals who receive undesirable outcomes from machine learning systems with minimum-cost improvements to achieve a desirable outcome. However, machine learning models often get updated, so the recourse may…