Kilian Q. Weinberger

Densely Connected Convolutional Networks

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections—one between each layer and its subsequent layer—our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less memory and computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet.

Unsupervised Learning of Image Manifolds by Semidefinite Programming

Can we detect low dimensional structure in high dimensional data sets of images? In this paper, we propose an algorithm for unsupervised learning of image manifolds by semidefinite programming. Given a data set of images, our algorithm computes a low dimensional representation of each image with the property that distances between nearby images are preserved. More generally, it can be used to analyze high dimensional data that lies on or near a low dimensional manifold. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.

Feature hashing for large scale multitask learning

Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction between random subspaces is negligible with high probability. We demonstrate the feasibility of this approach with experimental results for a new use case --- multitask learning with hundreds of thousands of tasks.

Unsupervised learning of image manifolds by semidefinite programming

Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be used to analyze high dimensional data that lies on or near a low dimensional manifold. It overcomes certain limitations of previous work in manifold learning, such as Isomap and locally linear embedding. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.

Deep Networks with Stochastic Depth

Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very deep networks comes with its own set of challenges. The gradients can vanish, the forward flow often diminishes, and the training time can be painfully slow. To address these problems, we propose stochastic depth, a training procedure that enables the seemingly contradictory setup to train short networks and use deep networks at test time. We start with very deep networks but during training, for each mini-batch, randomly drop a subset of layers and bypass them with the identity function. This simple approach complements the recent success of residual networks. It reduces training time substantially and improves the test error significantly on almost all data sets that we used for evaluation. With stochastic depth we can increase the depth of residual networks even beyond 1200 layers and still yield meaningful improvements in test error (4.91 % on CIFAR-10).

Fast solvers and efficient implementations for distance metric learning

In this paper we study how to improve nearest neighbor classification by learning a Mahalanobis distance metric. We build on a recently proposed framework for distance metric learning known as large margin nearest neighbor (LMNN) classification. Our paper makes three contributions. First, we describe a highly efficient solver for the particular instance of semidefinite programming that arises in LMNN classification; our solver can handle problems with billions of large margin constraints in a few hours. Second, we show how to reduce both training and testing times using metric ball trees; the speedups from ball trees are further magnified by learning low dimensional representations of the input space. Third, we show how to learn different Mahalanobis distance metrics in different parts of the input space. For large data sets, the use of locally adaptive distance metrics leads to even lower error rates.

Learning to rank with (a lot of) word features

In this article we present Supervised Semantic Indexing which defines a class of nonlinear (quadratic) models that are discriminatively trained to directly map from the word content in a query-document or document-document pair to a ranking score. Like Latent Semantic Indexing (LSI), our models take account of correlations between words (synonymy, polysemy). However, unlike LSI our models are trained from a supervised signal directly on the ranking task of interest, which we argue is the reason for our superior results. As the query and target texts are modeled separately, our approach is easily generalized to different retrieval tasks, such as cross-language retrieval or online advertising placement. Dealing with models on all pairs of words features is computationally challenging. We propose several improvements to our basic model for addressing this issue, including low rank (but diagonal preserving) representations, correlated feature hashing and sparsification. We provide an empirical study of all these methods on retrieval tasks based on Wikipedia documents as well as an Internet advertisement task. We obtain state-of-the-art performance while providing realistically scalable methods.

Supervised semantic indexing

In this article we propose Supervised Semantic Indexing (SSI), an algorithm that is trained on (query, document) pairs of text documents to predict the quality of their match. Like Latent Semantic Indexing (LSI), our models take account of correlations between words (synonymy, polysemy). However, unlike LSI our models are trained with a supervised signal directly on the ranking task of interest, which we argue is the reason for our superior results. As the query and target texts are modeled separately, our approach is easily generalized to different retrieval tasks, such as online advertising placement. Dealing with models on all pairs of words features is computationally challenging. We propose several improvements to our basic model for addressing this issue, including low rank (but diagonal preserving) representations, and correlated feature hashing (CFH). We provide an empirical study of all these methods on retrieval tasks based on Wikipedia documents as well as an Internet advertisement task. We obtain state-of-the-art performance while providing realistically scalable methods.

Parallel boosted regression trees for web search ranking

Gradient Boosted Regression Trees (GBRT) are the current state-of-the-art learning paradigm for machine learned web-search ranking - a domain notorious for very large data sets. In this paper, we propose a novel method for parallelizing the training of GBRT. Our technique parallelizes the construction of the individual regression trees and operates using the master-worker paradigm as follows. The data are partitioned among the workers. At each iteration, the worker summarizes its data-partition using histograms. The master processor uses these to build one layer of a regression tree, and then sends this layer to the workers, allowing the workers to build histograms for the next layer. Our algorithm carefully orchestrates overlap between communication and computation to achieve good performance. Since this approach is based on data partitioning, and requires a small amount of communication, it generalizes to distributed and shared memory machines, as well as clouds. We present experimental results on both shared memory machines and clusters for two large scale web search ranking data sets. We demonstrate that the loss in accuracy induced due to the histogram approximation in the regression tree creation can be compensated for through slightly deeper trees. As a result, we see no significant loss in accuracy on the Yahoo data sets and a very small reduction in accuracy for the Microsoft LETOR data. In addition, on shared memory machines, we obtain almost perfect linear speed-up with up to about 48 cores on the large data sets. On distributed memory machines, we get a speedup of 25 with 32 processors. Due to data partitioning our approach can scale to even larger data sets, on which one can reasonably expect even higher speedups.

Multi-task learning for boosting with application to web search ranking

In this paper we propose a novel algorithm for multi-task learning with boosted decision trees. We learn several different learning tasks with a joint model, explicitly addressing the specifics of each learning task with task-specific parameters and the commonalities between them through shared parameters. This enables implicit data sharing and regularization. We evaluate our learning method on web-search ranking data sets from several countries. Here, multitask learning is particularly helpful as data sets from different countries vary largely in size because of the cost of editorial judgments. Our experiments validate that learning various tasks jointly can lead to significant improvements in performance with surprising reliability.