IBM models are very important word alignment models in Machine Translation. Following the Maximum Likelihood Estimation principle to estimate their parameters, the models will easily overfit the training data when the data are sparse. While smoothing is a very popular solution in Language Model, there still lacks studies on smoothing for word alignment. In this paper, we propose a framework which generalizes the notable work Moore [2004] of applying additive smoothing to word alignment models. The framework allows developers to customize the smoothing amount for each pair of word. The added amount will be scaled appropriately by a common factor which reflects how much the framework trusts the adding strategy according to the performance on data. We also carefully examine various performance criteria and propose a smoothened version of the error count, which generally gives the best result.
Smoothing is a popular technique to solve the problem of sparsity. Language Model, which is another problem of Machine Translation, has a variety of smoothing methods. The classic paper @cite_11 gives a very good study of this solution for the Language Model problem. A large number of smoothing methods with extensive comparisons amongst them will be analyzed carefully in the paper.
@cite_11
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Language modeling approaches to information retrieval are attractive and promising because they connect the problem of retrieval with that of language model estimation, which has been studied extensively in other application areas such as speech recognition. The basic idea of these approaches is to estimate a language model for each document, and then rank documents by the likelihood of the query according to the estimated language model. A core problem in language model estimation is smoothing , which adjusts the maximum likelihood estimator so as to correct the inaccuracy due to data sparseness. In this paper, we study the problem of language model smoothing and its influence on retrieval performance. We examine the sensitivity of retrieval performance to the smoothing parameters and compare several popular smoothing methods on different test collections. Recurrent neural networks (RNNs) are a very recent technique to model long range dependencies in natural languages. They have clearly outperformed trigrams and other more advanced language modeling techniques by using non-linearly modeling long range dependencies. An alternative is to use log-linear interpolation of skip models (i.e. skip bigrams and skip trigrams). The method as such has been published earlier. In this paper we investigate the impact of different smoothing techniques on the skip models as a measure of their overall performance. One option is to use automatically trained distance clusters (both hard and soft) to increase robustness and to combat sparseness in the skip model. We also investigate alternative smoothing techniques on word level. For skip bigrams when skipping a small number of words Kneser-Ney smoothing (KN) is advantageous. For a larger number of words being skipped Dirichlet smoothing performs better. In order to exploit the advantages of both KN and Dirichlet smoothing we propose a new unified smoothing technique. Experiments are performed on four Babel languages: Cantonese, Pashto, Tagalog and Turkish. RNNs and log-linearly interpolated skip models are on par if the skip models are trained with standard smoothing techniques. Using the improved smoothing of the skip models along with distance clusters, we can clearly outperform RNNs by about 8-11 in perplexity across all four languages. We survey the most widely-used algorithms for smoothing models for language n -gram modeling. We then present an extensive empirical comparison of several of these smoothing techniques, including those described by Jelinek and Mercer (1980); Katz (1987); Bell, Cleary and Witten (1990); Ney, Essen and Kneser (1994), and Kneser and Ney (1995). We investigate how factors such as training data size, training corpus (e.g. Brown vs. Wall Street Journal), count cutoffs, and n -gram order (bigram vs. trigram) affect the relative performance of these methods, which is measured through the cross-entropy of test data. We find that these factors can significantly affect the relative performance of models, with the most significant factor being training data size. Since no previous comparisons have examined these factors systematically, this is the first thorough characterization of the relative performance of various algorithms. In addition, we introduce methodologies for analyzing smoothing algorithm efficacy in detail, and using these techniques we motivate a novel variation of Kneser?Ney smoothing that consistently outperforms all other algorithms evaluated. Finally, results showing that improved language model smoothing leads to improved speech recognition performance are presented. We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates. Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems. We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems. Training corpora for stochastic language models are virtually always too small for maximum-likelihood estimation, so smoothing the models is of great importance. The authors derive the cooccurrence smoothing technique for stochastic language modeling and give experimental evidence for its validity. Using word-bigram language models, cooccurrence smoothing improved the test-set perplexity by 14 on a German 100000-word text corpus and by 10 on an English 1-million word corpus. > Research in speech recognition and machine translation is boosting the use of large scale n-gram language models. We present an open source toolkit that permits to efficiently handle language models with billions of n-grams on conventional machines. The IRSTLM toolkit supports distribution of ngram collection and smoothing over a computer cluster, language model compression through probability quantization, lazy-loading of huge language models from disk. IRSTLM has been so far successfully deployed with the Moses toolkit for statistical machine translation and with the FBK-irst speech recognition system. Efficiency of the tool is reported on a speech transcription task of Italian political speeches using a language model of 1.1 billion four-grams. This paper presents a novel approach to stabilize video sequences based on a 3D perspective camera model. Compared to previous methods which are based on simplified models, our stabilization system can work in situations where significant depth variations exist in the scenes and the camera undergoes large translational movement. We formulate the stabilization problem as a quadratic cost function on smoothness and similarity constraints. This allows us to precisely control the smoothness by solving a sparse linear system of equations. By taking advantage of the sparseness, our optimization process is very efficient. Instead of recovering dense depths, we use approximate geometry representation and analyze the resulting warping errors. We show that by appropriately constraining warping error, visually plausible results can be achieved even using planar structures. A variety of experiments have been implemented, which demonstrates the robustness and efficiency of our approach. We study nonconvex distributed optimization in multiagent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and nonseparable) function—the agents’ sum-utility—plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on successive convex approximation techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents: each agent first solves (possibly inexactly) a local convex approximation of the nonconvex original problem, and then performs local averaging operations. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Our algorithmic framework is then customized to a variety of convex and nonconvex problems in several fields, including signal processing, communications, networking, and machine learning. Numerical results show that the new method compares favorably to existing distributed algorithms on both convex and nonconvex problems. We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlapping-group-lasso penalty, generalized from the group-lasso penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the fused-lasso penalty. For both types of penalties, due to their nonseparability and nonsmoothness, developing an efficient optimization method remains a challenging problem. In this paper we propose a general optimization approach, the smoothing proximal gradient (SPG) method, which can solve structured sparse regression problems with any smooth convex loss under a wide spectrum of structured sparsity-inducing penalties. Our approach combines a smoothing technique with an effective proximal gradient method. It achieves a convergence rate significantly faster than the standard first-order methods, subgradient methods, and is much more scalable than the most widely used interior-point methods. The efficiency and scalability of our method are demonstrated on both simulation experiments and real genetic data sets. We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a non-smooth regularisation penalty. The proposed algorithm, called Semi-Proximal Mirror-Prox, leverages the Fenchel-type representation of one part of the objective while handling the other part of the objective via linear minimization over the domain. The algorithm stands in contrast with more classical proximal gradient algorithms with smoothing, which require the computation of proximal operators at each iteration and can therefore be impractical for high-dimensional problems. We establish the theoretical convergence rate of Semi-Proximal Mirror-Prox, which exhibits the optimal complexity bounds, i.e. @math , for the number of calls to linear minimization oracle. We present promising experimental results showing the interest of the approach in comparison to competing methods. We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite programs and hence can be readily applied to a variety of machine learning problems. We show experimental results on three machine learning problems. Our approach outperforms state-of-the-art algorithms. We initiate the study of numerical linear algebra in the sliding window model, where only the most recent @math updates in the data stream form the underlying set. Although most existing work in the sliding window model uses the smooth histogram framework, most interesting linear-algebraic problems are not smooth; we show that the spectral norm, vector induced matrix norms, generalized regression, and low-rank approximation are not amenable for the smooth histogram framework. To overcome this challenge, we first give a deterministic algorithm that achieves spectral approximation in the sliding window model that can be viewed as a generalization of smooth histograms, using the Loewner ordering of PSD matrices. We then give algorithms for both spectral approximation and low-rank approximation that are space-optimal up to polylogarithmic factors. Our algorithms are based on a new notion of "reverse online" leverage scores that account for both how unique and how recent a row is, while preserving sparsity so that both our algorithms run in input sparsity runtime, up to lower order factors. We show that our techniques have applications to linear-algebraic problems in other settings. Specifically, we show that our analysis immediately implies an algorithm for low-rank approximation in the online setting that is space-optimal up to logarithmic factors, as well as nearly input sparsity time. We show our deterministic spectral approximation algorithm can be used to handle @math spectral approximation in the sliding window model under a certain assumption on the bit complexity of the entries. Finally, we show that our downsampling framework can be applied to the problem of approximate matrix multiplication and provide upper and lower bounds that are tight up to @math factors. In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply Nesterov's smooth optimization technique [Y. E. Nesterov, Dokl. Akad. Nauk SSSR, 269 (1983), pp. 543-547; Y. E. Nesterov, Math. Programming, 103 (2005), pp. 127-152] to their dual counterparts that are smooth convex problems. It is shown that the resulting approach has @math iteration complexity for finding an @math -optimal solution to both primal and dual problems. We then discuss the application of this approach to sparse covariance selection that is approximately solved as an @math -norm penalized maximum likelihood estimation problem, and also propose a variant of this approach which has substantially outperformed the latter one in our computational experiments. We finally compare the performance of these approaches with other first-order methods, namely, Nesterov's @math smooth approximation scheme and block-coordinate descent method studied in [A. d'Aspremont, O. Banerjee, and L. El Ghaoui, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 56-66; J. Friedman, T. Hastie, and R. Tibshirani, Biostatistics, 9 (2008), pp. 432-441] for sparse covariance selection on a set of randomly generated instances. It shows that our smooth optimization approach substantially outperforms the first method above, and moreover, its variant substantially outperforms both methods above. Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted @math -penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view. We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as a strong regularizer in supervised learning. Furthermore, we connect a maximum entropy based confidence penalty to label smoothing through the direction of the KL divergence. We exhaustively evaluate the proposed confidence penalty and label smoothing on 6 common benchmarks: image classification (MNIST and Cifar-10), language modeling (Penn Treebank), machine translation (WMT'14 English-to-German), and speech recognition (TIMIT and WSJ). We find that both label smoothing and the confidence penalty improve state-of-the-art models across benchmarks without modifying existing hyperparameters, suggesting the wide applicability of these regularizers. Machine learning has been successfully applied to complex network analysis in various areas, and graph neural networks (GNNs) based methods outperform others. Recently, adversarial attack on networks has attracted special attention since carefully crafted adversarial networks with slight perturbations on clean network may invalid lots of network applications, such as node classification, link prediction, and community detection etc. Such attacks are easily constructed with serious security threat to various analyze methods, including traditional methods and deep models. To the best of our knowledge, it is the first time that defense method against network adversarial attack is discussed. In this paper, we are interested in the possibility of defense against adversarial attack on network, and propose defense strategies for GNNs against attacks. First, we propose novel adversarial training strategies to improve GNNs' defensibility against attacks. Then, we analytically investigate the robustness properties for GNNs granted by the use of smooth defense, and propose two special smooth defense strategies: smoothing distillation and smoothing cross-entropy loss function. Both of them are capable of smoothing gradient of GNNs, and consequently reduce the amplitude of adversarial gradients, which benefits gradient masking from attackers. The comprehensive experiments show that our proposed strategies have great defensibility against different adversarial attacks on four real-world networks in different network analyze tasks. This paper considers an important class of convex programming (CP) problems, namely, the stochastic composite optimization (SCO), whose objective function is given by the summation of general nonsmooth and smooth stochastic components. Since SCO covers non-smooth, smooth and stochastic CP as certain special cases, a valid lower bound on the rate of convergence for solving these problems is known from the classic complexity theory of convex programming. Note however that the optimization algorithms that can achieve this lower bound had never been developed. In this paper, we show that the simple mirror-descent stochastic approximation method exhibits the best-known rate of convergence for solving these problems. Our major contribution is to introduce the accelerated stochastic approximation (AC-SA) algorithm based on Nesterov’s optimal method for smooth CP (Nesterov in Doklady AN SSSR 269:543–547, 1983; Nesterov in Math Program 103:127–152, 2005), and show that the AC-SA algorithm can achieve the aforementioned lower bound on the rate of convergence for SCO. To the best of our knowledge, it is also the first universally optimal algorithm in the literature for solving non-smooth, smooth and stochastic CP problems. We illustrate the significant advantages of the AC-SA algorithm over existing methods in the context of solving a special but broad class of stochastic programming problems. In this paper we present Jam, an extension of the Java language supporting mixins, that is, parametric heir classes. A mixin declaration in Jam is similar to a Java heir class declaration, except that it does not extend a fixed parent class, but simply specifies the set of fields and methods a generic parent should provide. In this way, the same mixin can be instantiated on many parent classes, producing different heirs, thus avoiding code duplication and largely improving modularity and reuse. Moreover, as happens for classes and interfaces, mixin names are reference types, and all the classes obtained by instantiating the same mixin are considered subtypes of the corresponding type, and hence can be handled in a uniform way through the common interface. This possibility allows a programming style where different ingredients are "mixed" together in defining a class; this paradigm is somewhat similar to that based on multiple inheritance, but avoids its complication.The language has been designed with the main objective in mind to obtain, rather than a new theoretical language, a working and smooth extension of Java. That means, on the design side, that we have faced the challenging problem of integrating the Java overall principles and complex type system with this new notion; on the implementation side, it means that we have developed a Jam-to-Java translator which makes Jam sources executable on every Java Virtual Machine. Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on ℝN with smoothness of order s can in general be captured with accuracy at most O(n−s N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x)=g(a⋅x) when both a∈ℝN and g∈C[0,1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g∈Cs[0,1]. We also study the role of sparsity or compressibility of a in such query problems.