We present a novel enhanced cyclic coordinate descent (ECCD) framework for solving generalized linear models with elastic net constraints that reduces training time in comparison to existing state-of-the-art methods. We redesign the CD method by performing a Taylor expansion around the current iterate to avoid nonlinear operations arising in the gradient computation. By introducing this approximation we are able to unroll the vector recurrences occurring in the CD method and reformulate the resulting computations into more efficient batched computations. We show empirically that the recurrence can be unrolled by a tunable integer parameter, s, such that s > 1 yields performance improvements without affecting convergence, whereas s= 1 yields the original CD method. A key advantage of ECCD is that it avoids the convergence delay and numerical instability exhibited by block coordinate descent. Finally, we implement our proposed method in C++ using Eigen to accelerate linear algebra computations. Comparison of our method against existing state-of-the-art solvers show consistent performance improvements of 3 in average for regularization path variant on diverse benchmark datasets. Our implementation is available at https://github.

The Poisson Generalized Linear Model (GLM) is a foundational tool for analyzing neural spike train data. However, standard implementations rely on discretizing spike times into binned count data, limiting temporal resolution and scalability. Here, we develop Monte Carlo (MC) methods and polynomial approximations (PA) to the continuous-time analog of these models, and show them to be advantageous over their discrete-time counterparts. Further, we propose using a set of exponentially scaled Laguerre polynomials as an orthogonal temporal basis, which improves filter identification and yields closed-form integral solutions under the polynomial approximation. Applied to both synthetic and real spike-time data from rodent hippocampus, our methods demonstrate superior accuracy and scalability compared to traditional binned GLMs, enabling functional connectivity inference in large-scale neural recordings that are temporally precise on the order of synaptic dynamical timescales and in agreement with known anatomical properties of hippocampal subregions. We provide open-source implementations of both MC and PA estimators, optimized for GPU acceleration, to facilitate adoption in the neuroscience community1.

We study the problem of efficiently estimating the coefficients of generalized linear models (GLMs) in the large-scale setting where the number of observations n is much larger than the number of predictors p, i.e. n p 1. We show that in GLMs with random (not necessarily Gaussian) design, the GLM coefficients are approximately proportional to the corresponding ordinary least squares (OLS) coefficients. Using this relation, we design an algorithm that achieves the same accuracy as the maximum likelihood estimator (MLE) through iterations that attain up to a cubic convergence rate, and that are cheaper than any batch optimization algorithm by at least a factor of O(p). We provide theoretical guarantees for our algorithm, and analyze the convergence behavior in terms of data dimensions. Finally, we demonstrate the performance of our algorithm through extensive numerical studies on large-scale real and synthetic datasets, and show that it achieves the highest performance compared to several other widely used optimization algorithms.

We study the problem of efficiently estimating the coefficients of generalized linear models (GLMs) in the large-scale setting where the number of observations $n$ is much larger than the number of predictors $p$, i.e. $n\gg p \gg 1$. We show that in GLMs with random (not necessarily Gaussian) design, the GLM coefficients are approximately proportional to the corresponding ordinary least squares (OLS) coefficients. Using this relation, we design an algorithm that achieves the same accuracy as the maximum likelihood estimator (MLE) through iterations that attain up to a cubic convergence rate, and that are cheaper than any batch optimization algorithm by at least a factor of $\mathcal{O}(p)$. We provide theoretical guarantees for our algorithm, and analyze the convergence behavior in terms of data dimensions.

OFUGLB outperforms or is at par with prior algorithms for logistic bandits.

Generative Language Models (GLMs) have shown impressive performance in tasks such as text generation, understanding, and reasoning. However, the large model size poses challenges for practical deployment.

Taking = p / gives the desired claim. Claim 2.7, we know that the multicalibration violation for The inequalities follow by Holder's inequality and the assumed bound on the weight of Recall that Cov[ y, z ]= E [ yz ] E [ y ] E [ z ] . Here, we give a high-level overview of the MCBoost algorithm of [ 20 ] and weak agnostic learning. Algorithm 2 MCBoost Parameters: hypothesis class C and > 0 Given: Dataset S sampled from D Initialize: p ( x) 1 / 2 . By Lemma 3.8, we know that In this Appendix, we give a full account of the definitions and results stated in Section 4 .