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- Tong Zhang
- 2004

We study how closely the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. We show that such a classification scheme can be… (More)

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked good convergence analysis. This paper… (More)

- Tong Zhang, Bin Yu
- 2003

Boosting is one of the most significant advances in machine learning for classification and regression. In its original and computationally flexible version, boosting seeks to minimize empirically a loss function in a greedy fashion. The resulted estimator takes an additive function form and is built iteratively by applying a base estimator (or learner) to… (More)

- Tong Zhang
- 2008

We derive sharp performance bounds for least squares regression with L1 regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [Ann.over, the result leads to an extended view of feature selection that allows less restrictive conditions than some… (More)

- Junzhou Huang, Tong Zhang
- 2009

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the… (More)

- John Langford, Tong Zhang
- 2007

We present Epoch-Greedy, an algorithm for contextual multi-armed bandits (also known as bandits with side information). Epoch-Greedy has the following properties: 1. No knowledge of a time horizon T is necessary. 2. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. 3. The regret scales as O(T 2/3 S 1/3)… (More)

- Tong Zhang
- 2005

We consider an extension of-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In… (More)

- Daniel Hsu, Sham M Kakade, Tong Zhang
- 2012

This work provides exponential tail inequalities for sums of random matrices that depend only on intrinsic dimensions rather than explicit matrix dimensions. These tail inequalities are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even… (More)

- Tong Zhang, Vijay S Iyengar
- 2002

Recommender systems use historical data on user preferences and other available data on users (for example, demographics) and items (for example, taxonomy) to predict items a new user might like. Applications of these methods include recommending items for purchase and personalizing the browsing experience on a web-site. Collaborative filtering methods have… (More)

The rapid accumulation of biological networks poses new challenges and calls for powerful integrative analysis tools. Most existing methods capable of simultaneously analyzing a large number of networks were primarily designed for unweighted networks, and cannot easily be extended to weighted networks. However, it is known that transforming weighted into… (More)