We introduce a new framework for learning in severely resource-constrained settings. Our technique delicately amalgamates the representational richness of multiple linear predictors with the sparsity of Boolean relaxations, and thereby yields classifiers that are compact, interpretable, and accurate. We provide a rigorous formalism of the learning problem, and establish fast convergence of the ensuing algorithm via relaxation to a minimax saddle point objective.

A.4 EstimatingparameterswhenY(t)isunavailable New parameter estimators that leverage only the available data need to be derived whenY(t) is unavailable. The derivation goes as follows: first, we eliminateY(t) from the model equations. The squared error of the estimated parameters are shown in Figure 1. First, we estimated the parameters separately for each individual. Second, we performed statistical analysis to find associations between the estimated parameters and the demographic variables.

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time algorithms with optimal error guarantees for both these problems. Specifically, for Gaussian robust mean estimation on Rd with contamination parameter ϵ (0,ϵ0) for a small absolute constant ϵ0, we give an algorithm with sample complexity n = O(d/ϵ2) and almost linear runtime that approximates the target mean within ℓ2-error O(ϵ). This improves on prior work that achieved this error guarantee with polynomially suboptimal sample and time complexity. For robust linear regression, we give the first algorithm with sample complexity n = O(d/ϵ2) and almost linear runtime that approximates the target regressor within ℓ2-error O(ϵ). This is the first polynomial sample and time algorithm achieving the optimal error guarantee, answering an open question in the literature. At the technical level, we develop a methodology that yields almost-linear time algorithms for multi-directional filtering that may be of broader interest.

We describe a new software framework for fast training of generalized linear models. Theframework,named Snap Machine Learning (Snap ML), combines recent advances inmachine learning systems andalgorithms inanested manner to reflect the hierarchical architecture of modern computing systems.

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