arXiv subjects

Liwei Wang

Publications and source records attributed to Liwei Wang.

270 records · Page 15Linked to original sources

arXiv2017

Efficient Private ERM for Smooth Objectives

In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both $ε$-DP and $(ε, δ)$-DP. For non-convex but smooth objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient Descent) algorithm, which provably converges to a stationary point with privacy guarantee. Besides the expected utility bounds, we also provide guarantees in high probability form. Experiments demonstrate that our algorithm consistently outperforms existing method in both utility and running time.

cs.LG↗

arXiv2017

Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations

Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation usually focus on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrix. Here we are given a $d \times n$ binary matrix $A$ and a small integer $k$. The goal is to find two binary matrices $U$ and $V$ of sizes $d \times k$ and $k \times n$ respectively, so that the Frobenius norm of $A - U V$ is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The $\mathrm{GF}(2)$ model and the Boolean semiring model. Unlike low rank approximation of real matrix which can be efficiently solved by Singular Value Decomposition, approximation of binary matrix is $NP$-hard even for $k=1$. In this paper, we consider the problem of Column Subset Selection (CSS), in which one low rank matrix must be formed by $k$ columns of the data matrix. We characterize the approximation ratio of CSS for binary matrices. For $GF(2)$ model, we show the approximation ratio of CSS is bounded by $\frac{k}{2}+1+\frac{k}{2(2^k-1)}$ and this bound is asymptotically tight. For Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of one low rank matrix are generated from Boolean formulas operating bitwise on columns of the data matrix. We show the approximation ratio of GCSS is bounded by $2^{k-1}+1$, and the exponential dependency on $k$ is inherent.

cs.CC↗

arXiv2017

Quadratic Upper Bound for Recursive Teaching Dimension of Finite VC Classes

In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$, introduced by Zilles et al. (2011), is a combinatorial complexity measure characterized by the worst-case number of examples necessary to identify a concept in $\mathcal C$ according to the recursive teaching model. For any finite concept class $\mathcal C \subseteq \{0,1\}^n$ with $\mathrm{VCD}(\mathcal C)=d$, Simon & Zilles (2015) posed an open problem $\mathrm{RTD}(\mathcal C) = O(d)$, i.e., is RTD linearly upper bounded by VCD? Previously, the best known result is an exponential upper bound $\mathrm{RTD}(\mathcal C) = O(d \cdot 2^d)$, due to Chen et al. (2016). In this paper, we show a quadratic upper bound: $\mathrm{RTD}(\mathcal C) = O(d^2)$, much closer to an answer to the open problem. We also discuss the challenges in fully solving the problem.

cs.LG↗

arXiv2016

A Refined Analysis of LSH for Well-dispersed Data Points

Near neighbor problems are fundamental in algorithms for high-dimensional Euclidean spaces. While classical approaches suffer from the curse of dimensionality, locality sensitive hashing (LSH) can effectively solve a-approximate r-near neighbor problem, and has been proven to be optimal in the worst case. However, for real-world data sets, LSH can naturally benefit from well-dispersed data and low doubling dimension, leading to significantly improved performance. In this paper, we address this issue and propose a refined analyses for running time of approximating near neighbors queries via LSH. We characterize dispersion of data using N_b, the number of b*r-near pairs among the data points. Combined with optimal data-oblivious LSH scheme, we get a new query time bound depending on N_b and doubling dimension. For many natural scenarios where points are well-dispersed or lying in a low-doubling-dimension space, our result leads to sharper performance than existing worst-case analysis. This paper not only present first rigorous proof on how LSHs make use of the structure of data points, but also provide important insights into parameter setting in the practice of LSH beyond worst case. Besides, the techniques in our analysis involve a generalized version of sphere packing problem, which might be of some independent interest.

cs.DS↗

arXiv2016

Stable Memory Allocation in the Hippocampus: Fundamental Limits and Neural Realization

It is believed that hippocampus functions as a memory allocator in brain, the mechanism of which remains unrevealed. In Valiant's neuroidal model, the hippocampus was described as a randomly connected graph, the computation on which maps input to a set of activated neuroids with stable size. Valiant proposed three requirements for the hippocampal circuit to become a stable memory allocator (SMA): stability, continuity and orthogonality. The functionality of SMA in hippocampus is essential in further computation within cortex, according to Valiant's model. In this paper, we put these requirements for memorization functions into rigorous mathematical formulation and introduce the concept of capacity, based on the probability of erroneous allocation. We prove fundamental limits for the capacity and error probability of SMA, in both data-independent and data-dependent settings. We also establish an example of stable memory allocator that can be implemented via neuroidal circuits. Both theoretical bounds and simulation results show that the neural SMA functions well.

cs.NE↗

arXiv2016

Dual Learning for Machine Translation

While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training. However, human labeling is very costly. To tackle this training data bottleneck, we develop a dual-learning mechanism, which can enable an NMT system to automatically learn from unlabeled data through a dual-learning game. This mechanism is inspired by the following observation: any machine translation task has a dual task, e.g., English-to-French translation (primal) versus French-to-English translation (dual); the primal and dual tasks can form a closed loop, and generate informative feedback signals to train the translation models, even if without the involvement of a human labeler. In the dual-learning mechanism, we use one agent to represent the model for the primal task and the other agent to represent the model for the dual task, then ask them to teach each other through a reinforcement learning process. Based on the feedback signals generated during this process (e.g., the language-model likelihood of the output of a model, and the reconstruction error of the original sentence after the primal and dual translations), we can iteratively update the two models until convergence (e.g., using the policy gradient methods). We call the corresponding approach to neural machine translation \emph{dual-NMT}. Experiments show that dual-NMT works very well on English$\leftrightarrow$French translation; especially, by learning from monolingual data (with 10% bilingual data for warm start), it achieves a comparable accuracy to NMT trained from the full bilingual data for the French-to-English translation task.

cs.CL↗

arXiv2016

Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models

The Flickr30k dataset has become a standard benchmark for sentence-based image description. This paper presents Flickr30k Entities, which augments the 158k captions from Flickr30k with 244k coreference chains, linking mentions of the same entities across different captions for the same image, and associating them with 276k manually annotated bounding boxes. Such annotations are essential for continued progress in automatic image description and grounded language understanding. They enable us to define a new benchmark for localization of textual entity mentions in an image. We present a strong baseline for this task that combines an image-text embedding, detectors for common objects, a color classifier, and a bias towards selecting larger objects. While our baseline rivals in accuracy more complex state-of-the-art models, we show that its gains cannot be easily parlayed into improvements on such tasks as image-sentence retrieval, thus underlining the limitations of current methods and the need for further research.

cs.CV↗

arXiv2016

Learning Deep Structure-Preserving Image-Text Embeddings

This paper proposes a method for learning joint embeddings of images and text using a two-branch neural network with multiple layers of linear projections followed by nonlinearities. The network is trained using a large margin objective that combines cross-view ranking constraints with within-view neighborhood structure preservation constraints inspired by metric learning literature. Extensive experiments show that our approach gains significant improvements in accuracy for image-to-text and text-to-image retrieval. Our method achieves new state-of-the-art results on the Flickr30K and MSCOCO image-sentence datasets and shows promise on the new task of phrase localization on the Flickr30K Entities dataset.

cs.CV↗

arXiv2015

On the Depth of Deep Neural Networks: A Theoretical View

People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (measured by Betti numbers based complexity) than shallower networks in multi-class setting, and thus can lead to smaller empirical margin error. This implies positive impact of depth. The combination of these two results shows that for DNN with restricted number of hidden units, increasing depth is not always good since there is a tradeoff between positive and negative impacts. These results inspire us to seek alternative ways to achieve positive impact of depth, e.g., imposing margin-based penalty terms to cross entropy loss so as to reduce empirical margin error without increasing depth. Our experiments show that in this way, we achieve significantly better test performance.

cs.LG↗

arXiv2015

Training Deeper Convolutional Networks with Deep Supervision

One of the most promising ways of improving the performance of deep convolutional neural networks is by increasing the number of convolutional layers. However, adding layers makes training more difficult and computationally expensive. In order to train deeper networks, we propose to add auxiliary supervision branches after certain intermediate layers during training. We formulate a simple rule of thumb to determine where these branches should be added. The resulting deeply supervised structure makes the training much easier and also produces better classification results on ImageNet and the recently released, larger MIT Places dataset

cs.CV↗

arXiv2015

Pairwise Constraint Propagation on Multi-View Data

This paper presents a graph-based learning approach to pairwise constraint propagation on multi-view data. Although pairwise constraint propagation has been studied extensively, pairwise constraints are usually defined over pairs of data points from a single view, i.e., only intra-view constraint propagation is considered for multi-view tasks. In fact, very little attention has been paid to inter-view constraint propagation, which is more challenging since pairwise constraints are now defined over pairs of data points from different views. In this paper, we propose to decompose the challenging inter-view constraint propagation problem into semi-supervised learning subproblems so that they can be efficiently solved based on graph-based label propagation. To the best of our knowledge, this is the first attempt to give an efficient solution to inter-view constraint propagation from a semi-supervised learning viewpoint. Moreover, since graph-based label propagation has been adopted for basic optimization, we develop two constrained graph construction methods for interview constraint propagation, which only differ in how the intra-view pairwise constraints are exploited. The experimental results in cross-view retrieval have shown the promising performance of our inter-view constraint propagation.

cs.CV↗

arXiv2015

Image classification by visual bag-of-words refinement and reduction

This paper presents a new framework for visual bag-of-words (BOW) refinement and reduction to overcome the drawbacks associated with the visual BOW model which has been widely used for image classification. Although very influential in the literature, the traditional visual BOW model has two distinct drawbacks. Firstly, for efficiency purposes, the visual vocabulary is commonly constructed by directly clustering the low-level visual feature vectors extracted from local keypoints, without considering the high-level semantics of images. That is, the visual BOW model still suffers from the semantic gap, and thus may lead to significant performance degradation in more challenging tasks (e.g. social image classification). Secondly, typically thousands of visual words are generated to obtain better performance on a relatively large image dataset. Due to such large vocabulary size, the subsequent image classification may take sheer amount of time. To overcome the first drawback, we develop a graph-based method for visual BOW refinement by exploiting the tags (easy to access although noisy) of social images. More notably, for efficient image classification, we further reduce the refined visual BOW model to a much smaller size through semantic spectral clustering. Extensive experimental results show the promising performance of the proposed framework for visual BOW refinement and reduction.

cs.CV↗

arXiv2014

Can Image-Level Labels Replace Pixel-Level Labels for Image Parsing

This paper presents a weakly supervised sparse learning approach to the problem of noisily tagged image parsing, or segmenting all the objects within a noisily tagged image and identifying their categories (i.e. tags). Different from the traditional image parsing that takes pixel-level labels as strong supervisory information, our noisily tagged image parsing is provided with noisy tags of all the images (i.e. image-level labels), which is a natural setting for social image collections (e.g. Flickr). By oversegmenting all the images into regions, we formulate noisily tagged image parsing as a weakly supervised sparse learning problem over all the regions, where the initial labels of each region are inferred from image-level labels. Furthermore, we develop an efficient algorithm to solve such weakly supervised sparse learning problem. The experimental results on two benchmark datasets show the effectiveness of our approach. More notably, the reported surprising results shed some light on answering the question: can image-level labels replace pixel-level labels (hard to access) as supervisory information for image parsing.

cs.CV↗

arXiv2014

Multi-scale Orderless Pooling of Deep Convolutional Activation Features

Deep convolutional neural networks (CNN) have shown their promise as a universal representation for recognition. However, global CNN activations lack geometric invariance, which limits their robustness for classification and matching of highly variable scenes. To improve the invariance of CNN activations without degrading their discriminative power, this paper presents a simple but effective scheme called multi-scale orderless pooling (MOP-CNN). This scheme extracts CNN activations for local patches at multiple scale levels, performs orderless VLAD pooling of these activations at each level separately, and concatenates the result. The resulting MOP-CNN representation can be used as a generic feature for either supervised or unsupervised recognition tasks, from image classification to instance-level retrieval; it consistently outperforms global CNN activations without requiring any joint training of prediction layers for a particular target dataset. In absolute terms, it achieves state-of-the-art results on the challenging SUN397 and MIT Indoor Scenes classification datasets, and competitive results on ILSVRC2012/2013 classification and INRIA Holidays retrieval datasets.

cs.CV↗

arXiv2014

A Game-theoretic Machine Learning Approach for Revenue Maximization in Sponsored Search

Sponsored search is an important monetization channel for search engines, in which an auction mechanism is used to select the ads shown to users and determine the prices charged from advertisers. There have been several pieces of work in the literature that investigate how to design an auction mechanism in order to optimize the revenue of the search engine. However, due to some unrealistic assumptions used, the practical values of these studies are not very clear. In this paper, we propose a novel \emph{game-theoretic machine learning} approach, which naturally combines machine learning and game theory, and learns the auction mechanism using a bilevel optimization framework. In particular, we first learn a Markov model from historical data to describe how advertisers change their bids in response to an auction mechanism, and then for any given auction mechanism, we use the learnt model to predict its corresponding future bid sequences. Next we learn the auction mechanism through empirical revenue maximization on the predicted bid sequences. We show that the empirical revenue will converge when the prediction period approaches infinity, and a Genetic Programming algorithm can effectively optimize this empirical revenue. Our experiments indicate that the proposed approach is able to produce a much more effective auction mechanism than several baselines.

cs.GT↗

arXiv2014

Generalized Second Price Auction with Probabilistic Broad Match

Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this issue, we propose a novel broad-match mechanism, which we call the Probabilistic Broad-Match (PBM) mechanism. Different from SBM that puts together the ads bidding on all the keywords matched to a given query for the GSP auction, the GSP with PBM (denoted as PBM-GSP) randomly samples a keyword according to a predefined probability distribution and only runs the GSP auction for the ads bidding on this sampled keyword. We perform a comprehensive study on the theoretical properties of the PBM-GSP. Specifically, we study its social welfare in the worst equilibrium, in both full-information and Bayesian settings. The results show that PBM-GSP can generate larger welfare than SBM-GSP under mild conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in Bayesian setting. To the best of our knowledge, this is the first work on broad-match mechanisms for GSP that goes beyond the single-slot case and the full-information setting.

cs.GT↗

arXiv2014

Differentially Private Data Releasing for Smooth Queries with Synthetic Database Output

We consider accurately answering smooth queries while preserving differential privacy. A query is said to be $K$-smooth if it is specified by a function defined on $[-1,1]^d$ whose partial derivatives up to order $K$ are all bounded. We develop an $ε$-differentially private mechanism for the class of $K$-smooth queries. The major advantage of the algorithm is that it outputs a synthetic database. In real applications, a synthetic database output is appealing. Our mechanism achieves an accuracy of $O (n^{-\frac{K}{2d+K}}/ε)$, and runs in polynomial time. We also generalize the mechanism to preserve $(ε, δ)$-differential privacy with slightly improved accuracy. Extensive experiments on benchmark datasets demonstrate that the mechanisms have good accuracy and are efficient.

cs.DB↗

arXiv2013

A Theoretical Analysis of NDCG Type Ranking Measures

A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its theoretical properties. We first show that, whatever the ranking function is, the standard NDCG which adopts a logarithmic discount, converges to 1 as the number of items to rank goes to infinity. On the first sight, this result is very surprising. It seems to imply that NDCG cannot differentiate good and bad ranking functions, contradicting to the empirical success of NDCG in many applications. In order to have a deeper understanding of ranking measures in general, we propose a notion referred to as consistent distinguishability. This notion captures the intuition that a ranking measure should have such a property: For every pair of substantially different ranking functions, the ranking measure can decide which one is better in a consistent manner on almost all datasets. We show that NDCG with logarithmic discount has consistent distinguishability although it converges to the same limit for all ranking functions. We next characterize the set of all feasible discount functions for NDCG according to the concept of consistent distinguishability. Specifically we show that whether NDCG has consistent distinguishability depends on how fast the discount decays, and 1/r is a critical point. We then turn to the cut-off version of NDCG, i.e., NDCG@k. We analyze the distinguishability of NDCG@k for various choices of k and the discount functions. Experimental results on real Web search datasets agree well with the theory.

cs.LG↗