A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Optimal classification rules control error rates in multiclass mixture models.
problem Classifying observations in multiclass mixture models while controlling error rates.
method Finding optimal classification rules by searching an optimal region in the observation space, using Maximum A Posteriori (MAP) rule and heuristic computation.
result The FDR-like optimal rule can be significantly less conservative than thresholded MAP rules.
Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal Bayes classifier. To this end we propose a weighted nearest neighbor (WNN) graph es…
We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previ…
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention as been paid to proving lower error bounds for the SGD method. It is the key cont…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of n objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …
This paper studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of n vertices…
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be appl…
Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult to obtain via optimization due to sparse constraints in important function class…
This paper analyzes error feedback in compressed federated learning for non-convex optimization problems.
problem Reducing communication cost in federated learning with biased gradient compression.
method Proposes Fed-EF, a compressed federated learning scheme with error feedback, and analyzes its convergence rate and performance under partial client participation.
result Fed-EF can match the convergence rate of full-precision FL under data heterogeneity with a linear speedup and no extra slow-down factor due to stale error compensation.
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…
Crowdsourcing has become an effective and popular tool for human-powered computation to label large datasets. Since the workers can be unreliable, it is common in crowdsourcing to assign multiple workers to one task, and to aggregate the labels in order to obtain results of high quality. In this paper, we provide finit…
In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent …
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We …
In various approaches to learning, notably in domain adaptation, active learning, learning under covariate shift, semi-supervised learning, learning with concept drift, and the like, one often wants to compare a baseline classifier to one or more advanced (or at least different) strategies. In this chapter, we basicall…