Search arXivSearch

arXiv · 1812.10564

BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees

Abstract

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yongjoo Park, Jingyi Qing, Xiaoyang Shen, Barzan Mozafari. 2018-12-26. BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees. https://doi.org/10.1145/3299869.3300077

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

Classical particle methods based on propagation of chaos (PoC) have been developed for solving mean-field stochastic differential equations and their associated nonlinear Fokker--Planck equations. However, direct PoC implementations are difficult to apply to high-dimensional problems because they require simulating and storing large numbers of interacting particles, often with high particle-particle interaction costs. Motivated by these limitations, we build on the recently proposed sequential propagation of chaos (SPoC) framework, which replaces the fully interacting particle system in PoC with a sequential interaction mechanism. Based on this structure, we present DeepSPoC, a neural particle method that embeds a neural density representation into the sequential particle dynamics. DeepSPoC simulates particles batch by batch, while the neural network represents the evolving empirical law and is substituted into the coefficients of the mean-field SDE, thereby replacing direct particle-particle interactions with particle-network interactions. In DeepSPoC, a recently developed normalizing flow model called KRnet is used to approximate the empirical measure of particles. Compared with direct particle implementations, DeepSPoC substantially reduces memory consumption and evaluates interaction terms more efficiently, thereby improving scalability for high-dimensional problems. We apply DeepSPoC to a wide range of mean-field equations and verify its effectiveness and computational advantages.

cs.LG