Private Learning Implies Online Learning: An Efficient Reduction

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online learning from expert advice

ANALYZING BIG DATA WITH DECISION TREES

ANALYZING BIG DATA WITH DECISION TREE

Positive Semidefinite Metric Learning Using Boosting-like Algorithms

The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive definite. Semidefinite programming is often used to enforce this constraint, but does not scale well and easy to implement. BoostMetric is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting methods are easy to implement, efficient, and can accommodate various types of constraints. We extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor. Experiments on various datasets demonstrate that the proposed algorithms compare favorably to those state-of-the-art methods in terms of classification accuracy and running time.Comment: 30 pages, appearing in Journal of Machine Learning Researc

Boosted Random ferns for object detection

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper we introduce the Boosted Random Ferns (BRFs) to rapidly build discriminative classifiers for learning and detecting object categories. At the core of our approach we use standard random ferns, but we introduce four main innovations that let us bring ferns from an instance to a category level, and still retain efficiency. First, we define binary features on the histogram of oriented gradients-domain (as opposed to intensity-), allowing for a better representation of intra-class variability. Second, both the positions where ferns are evaluated within the sliding window, and the location of the binary features for each fern are not chosen completely at random, but instead we use a boosting strategy to pick the most discriminative combination of them. This is further enhanced by our third contribution, that is to adapt the boosting strategy to enable sharing of binary features among different ferns, yielding high recognition rates at a low computational cost. And finally, we show that training can be performed online, for sequentially arriving images. Overall, the resulting classifier can be very efficiently trained, densely evaluated for all image locations in about 0.1 seconds, and provides detection rates similar to competing approaches that require expensive and significantly slower processing times. We demonstrate the effectiveness of our approach by thorough experimentation in publicly available datasets in which we compare against state-of-the-art, and for tasks of both 2D detection and 3D multi-view estimation.Peer ReviewedPostprint (author's final draft

Generalization bounds for averaged classifiers

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted average of all hypotheses, weighted exponentially with respect to their training error. We show that the prediction of this algorithm is much more stable than the prediction of an algorithm that predicts with the best hypothesis. By allowing the algorithm to abstain from predicting on some examples, we show that the predictions it makes when it does not abstain are very reliable. Finally, we show that the probability that the algorithm abstains is comparable to the generalization error of the best hypothesis in the class.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000005