Tag: Machine Learning

Robust Frequent Directions with Application in Online Learning

JMLR Edit "Robust Frequent Directions with Application in Online Learning"
The frequent directions (FD) technique is a deterministic approach for online sketching that has many applications in machine learning. The conventional FD is a heuristic procedure that often outputs rank deficient matrices. To overcome the rank deficiency problem, we propose a new sketching strategy called robust frequent directions (RFD) by introducing a regularization term. RFD can be derived from an optimization problem. It updates the sketch matrix and the regularization term adaptively and jointly. RFD reduces the approximation error of FD without increasing the computational cost. We also apply RFD to online learning and propose an effective hyperparameter-free online Newton algorithm. We derive a regret bound for our online Newton algorithm based on RFD, which guarantees the robustness of the algorithm. The experimental studies demonstrate that the proposed method outperforms state-of-the-art second order online learning algorithms.

Iterated Learning in Dynamic Social Networks

JMLR Edit "Iterated Learning in Dynamic Social Networks"
A classic finding by (Kalish et al., 2007) shows that no language can be learned iteratively by rational agents in a self-sustained manner. In other words, if $A$ teaches a foreign language to $B$, who then teaches what she learned to $C$, and so on, the language will quickly get lost and agents will wind up teaching their own common native language. If so, how can linguistic novelty ever be sustained? We address this apparent paradox by considering the case of iterated learning in a social network: we show that by varying the lengths of the learning sessions over time or by keeping the networks dynamic, it is possible for iterated learning to endure forever with arbitrarily small loss.

Train and Test Tightness of LP Relaxations in Structured Prediction

JMLR Edit "Train and Test Tightness of LP Relaxations in Structured Prediction"
Structured prediction is used in areas including computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions required to obtain accurate predictions, both learning and inference typically require the use of approximate solvers. We propose a theoretical explanation for the striking observation that approximations based on linear programming (LP) relaxations are often tight (exact) on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that this training tightness generalizes to test data.

Picasso: A Sparse Learning Library for High Dimensional Data Analysis in R and Python

JMLR Edit "Picasso: A Sparse Learning Library for High Dimensional Data Analysis in R and Python"
We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson regression and scaled sparse linear regression) combined with efficient active set selection strategies. Besides, the library allows users to choose different sparsity-inducing regularizers, including the convex $\ell_1$, nonvoncex MCP and SCAD regularizers. The library is coded in \texttt{C++} and has user-friendly R and Python wrappers. Numerical experiments demonstrate that picasso can scale up to large problems efficiently.

Complete Search for Feature Selection in Decision Trees

JMLR Edit "Complete Search for Feature Selection in Decision Trees"
The search space for the feature selection problem in decision tree learning is the lattice of subsets of the available features. We design an exact enumeration procedure of the subsets of features that lead to all and only the distinct decision trees built by a greedy top-down decision tree induction algorithm. The procedure stores, in the worst case, a number of trees linear in the number of features. By exploiting a further pruning of the search space, we design a complete procedure for finding $\delta$-acceptable feature subsets, which depart by at most $\delta$ from the best estimated error over any feature subset. Feature subsets with the best estimated error are called best feature subsets. Our results apply to any error estimator function, but experiments are mainly conducted under the wrapper model, in which the misclassification error over a search set is used as an estimator. The approach is also adapted to the design of a computational optimization of the sequential backward elimination heuristic, extending its applicability to large dimensional datasets. The procedures of this paper are implemented in a multi-core data parallel C++ system. We investigate experimentally the properties and limitations of the procedures on a collection of 20 benchmark datasets, showing that oversearching increases both overfitting and instability.

PyOD: A Python Toolbox for Scalable Outlier Detection

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PyOD is an open-source Python toolbox for performing scalable outlier detection on multivariate data. Uniquely, it provides access to a wide range of outlier detection algorithms, including established outlier ensembles and more recent neural network-based approaches, under a single, well-documented API designed for use by both practitioners and researchers. With robustness and scalability in mind, best practices such as unit testing, continuous integration, code coverage, maintainability checks, interactive examples and parallelization are emphasized as core components in the toolbox's development. PyOD is compatible with both Python 2 and 3 and can be installed through Python Package Index (PyPI) or https://github.com/yzhao062/pyod.

Learning to Match via Inverse Optimal Transport

JMLR Edit "Learning to Match via Inverse Optimal Transport"
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching contexts. We emphasize that the discrete optimal transport plays the role of a variational principle which gives rise to an optimization based framework for modeling the observed empirical matching data. Our formulation leads to a non-convex optimization problem which can be solved efficiently by an alternating optimization method. A key novel aspect of our formulation is the incorporation of marginal relaxation via regularized Wasserstein distance, significantly improving the robustness of the method in the face of noisy or missing empirical matching data. Our model falls into the category of prescriptive models, which not only predict potential future matching, but is also able to explain what leads to empirical matching and quantifies the impact of changes in matching factors. The proposed approach has wide applicability including predicting matching in online dating, labor market, college application and crowdsourcing. We back up our claims with numerical experiments on both synthetic data and real world data sets.

Redundancy Techniques for Straggler Mitigation in Distributed Optimization and Learning

JMLR Edit "Redundancy Techniques for Straggler Mitigation in Distributed Optimization and Learning"
Performance of distributed optimization and learning systems is bottlenecked by “straggler” nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is “encoded” to have an over-complete representation with built-in redundancy, and the straggling nodes in the system are dynamically treated as missing, or as “erasures” at every iteration, whose loss is compensated by the embedded redundancy. For quadratic loss functions, we show that under a simple encoding scheme, many optimization algorithms (gradient descent, L-BFGS, and proximal gradient) operating under data parallelism converge to an approximate solution even when stragglers are ignored. Furthermore, we show a similar result for a wider class of convex loss functions when operating under model parallelism. The applicable classes of objectives covers several popular learning problems such as linear regression, LASSO, support vector machine, collaborative filtering, and generalized linear models including logistic regression. These convergence results are deterministic, i.e., they establish sample path convergence for arbitrary sequences of delay patterns or distributions on the nodes, and are independent of the tail behavior of the delay distribution. We demonstrate that equiangular tight frames have desirable properties as encoding matrices, and propose efficient mechanisms for encoding large-scale data. We implement the proposed technique on Amazon EC2 clusters, and demonstrate its performance over several learning problems, including matrix factorization, LASSO, ridge regression and logistic regression, and compare the proposed method with uncoded, asynchronous, and data replication strategies.

A Representer Theorem for Deep Kernel Learning

JMLR Edit "A Representer Theorem for Deep Kernel Learning"
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence in the finite-sample case, the corresponding infinite-dimensional minimization problems can be recast into (nonlinear) finite-dimensional minimization problems, which can be tackled with nonlinear optimization algorithms. Moreover, we show how concatenated machine learning problems can be reformulated as neural networks and how our representer theorem applies to a broad class of state-of-the-art deep learning methods.