On Correcting Inputs: Inverse Optimization for Online Structured Prediction

Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially in the context of online learning systems where the objective is to learn appropriate feature weights given some training samples. Such scenarios necessitate the study of inverse optimization problems where one is given an input instance as well as a desired output and the task is to adjust the input data so that the given output is indeed optimal. Motivated by learning structured prediction models, in this paper we consider inverse optimization with a margin, i.e., we require the given output to be better than all other feasible outputs by a desired margin. We consider such inverse optimization problems for maximum weight matroid basis, matroid intersection, perfect matchings, minimum cost maximum flows, and shortest paths and derive the first known results for such problems with a non-zero margin. The effectiveness of these algorithmic approaches to online learning for structured prediction is also discussed.Comment: Conference version to appear in FSTTCS, 201

Structured prediction models via the matrix-tree theorem

This paper provides an algorithmic framework for learning statistical models involving directed spanning trees, or equivalently non-projective dependency structures. We show how partition functions and marginals for directed spanning trees can be computed by an adaptation of Kirchhoff’s Matrix-Tree Theorem. To demonstrate an application of the method, we perform experiments which use the algorithm in training both log-linear and max-margin dependency parsers. The new training methods give improvements in accuracy over perceptron-trained models.Peer ReviewedPostprint (author’s final draft

Syntactic inductive biases for deep learning methods

Le débat entre connexionnisme et symbolisme est l'une des forces majeures qui animent le développement de l'Intelligence Artificielle. L'apprentissage profond et la linguistique théorique sont les domaines d'études les plus représentatifs pour les deux écoles respectivement. Alors que la méthode d'apprentissage profond a fait des percées impressionnantes et est devenue la principale raison de la récente prospérité de l'IA pour l'industrie et les universités, la linguistique et le symbolisme occupent quelque domaines importantes, notamment l'interprétabilité et la fiabilité. Dans cette thèse, nous essayons de construire une connexion entre les deux écoles en introduisant des biais inductifs linguistiques pour les modèles d'apprentissage profond. Nous proposons deux familles de biais inductifs, une pour la structure de circonscription et une autre pour la structure de dépendance. Le biais inductif de circonscription encourage les modèles d'apprentissage profond à utiliser différentes unités (ou neurones) pour traiter séparément les informations à long terme et à court terme. Cette séparation fournit un moyen pour les modèles d'apprentissage profond de construire les représentations hiérarchiques latentes à partir d'entrées séquentielles, dont une représentation de niveau supérieur est composée et peut être décomposée en une série de représentations de niveau inférieur. Par exemple, sans connaître la structure de vérité fondamentale, notre modèle proposé apprend à traiter l'expression logique en composant des représentations de variables et d'opérateurs en représentations d'expressions selon sa structure syntaxique. D'autre part, le biais inductif de dépendance encourage les modèles à trouver les relations latentes entre les mots dans la séquence d'entrée. Pour le langage naturel, les relations latentes sont généralement modélisées sous la forme d'un graphe de dépendance orienté, où un mot a exactement un nœud parent et zéro ou plusieurs nœuds enfants. Après avoir appliqué cette contrainte à un modèle de type transformateur, nous constatons que le modèle est capable d'induire des graphes orientés proches des annotations d'experts humains, et qu'il surpasse également le modèle de transformateur standard sur différentes tâches. Nous pensons que ces résultats expérimentaux démontrent une alternative intéressante pour le développement futur de modèles d'apprentissage profond.The debate between connectionism and symbolism is one of the major forces that drive the development of Artificial Intelligence. Deep Learning and theoretical linguistics are the most representative fields of study for the two schools respectively. While the deep learning method has made impressive breakthroughs and became the major reason behind the recent AI prosperity for industry and academia, linguistics and symbolism still holding some important grounds including reasoning, interpretability and reliability. In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for dependency structure. The constituency inductive bias encourages deep learning models to use different units (or neurons) to separately process long-term and short-term information. This separation provides a way for deep learning models to build the latent hierarchical representations from sequential inputs, that a higher-level representation is composed of and can be decomposed into a series of lower-level representations. For example, without knowing the ground-truth structure, our proposed model learns to process logical expression through composing representations of variables and operators into representations of expressions according to its syntactic structure. On the other hand, the dependency inductive bias encourages models to find the latent relations between entities in the input sequence. For natural language, the latent relations are usually modeled as a directed dependency graph, where a word has exactly one parent node and zero or several children nodes. After applying this constraint to a transformer-like model, we find the model is capable of inducing directed graphs that are close to human expert annotations, and it also outperforms the standard transformer model on different tasks. We believe that these experimental results demonstrate an interesting alternative for the future development of deep learning models

Efficient Lagrangian relaxation algorithms for exact inference in natural language tasks

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 95-99).For many tasks in natural language processing, finding the best solution requires a search over a large set of possible structures. Solving these combinatorial search problems exactly can be inefficient, and so researchers often use approximate techniques at the cost of model accuracy. In this thesis, we turn to Lagrangian relaxation as an alternative to approximate inference in natural language tasks. We demonstrate that Lagrangian relaxation algorithms provide efficient solutions while still maintaining formal guarantees. The approach leads to inference algorithms with the following properties: " The resulting algorithms are simple and efficient, building on standard combinatorial algorithms for relaxed problems. " The algorithms provably solve a linear programming (LP) relaxation of the original inference problem. " Empirically, the relaxation often leads to an exact solution to the original problem. We develop Lagrangian relaxation algorithms for several important tasks in natural language processing including higher-order non-projective dependency parsing, syntactic machine translation, integrated constituency and dependency parsing, and part-of-speech tagging with inter-sentence constraints. For each of these tasks, we show that the Lagrangian relaxation algorithms are often significantly faster than exact methods while finding the exact solution with a certificate of optimality in the vast majority of examples.by Alexander M. Rush.S.M

Features and Algorithms for Visual Parsing of Handwritten Mathematical Expressions

Math expressions are an essential part of scientific documents. Handwritten math expressions recognition can benefit human-computer interaction especially in the education domain and is a critical part of document recognition and analysis. Parsing the spatial arrangement of symbols is an essential part of math expression recognition. A variety of parsing techniques have been developed during the past three decades, and fall into two groups. The first group is graph-based parsing. It selects a path or sub-graph which obeys some rule to form a possible interpretation for the given expression. The second group is grammar driven parsing. Grammars and related parameters are defined manually for different tasks. The time complexity of these two groups parsing is high, and they often impose some strict constraints to reduce the computation. The aim of this thesis is working towards building a straightforward and effective parser with as few constraints as possible. First, we propose using a line of sight graph for representing the layout of strokes and symbols in math expressions. It achieves higher F-score than other graph representations and reduces search space for parsing. Second, we modify the shape context feature with Parzen window density estimation. This feature set works well for symbol segmentation, symbol classification and symbol layout analysis. We get a higher symbol segmentation F-score than other systems on CROHME 2014 dataset. Finally, we develop a Maximum Spanning Tree (MST) based parser using Edmonds\u27 algorithm, which extracts an MST from the directed line of sight graph in two passes: first symbols are segmented, and then symbols and spatial relationship are labeled. The time complexity of our MST-based parsing is lower than the time complexity of CYK parsing with context-free grammars. Also, our MST-based parsing obtains higher structure rate and expression rate than CYK parsing when symbol segmentation is accurate. Correct structure means we get the structure of the symbol layout tree correct, even though the label of the edge in the symbol layout tree might be wrong. The performance of our math expression recognition system with MST-based parsing is competitive on CROHME 2012 and 2014 datasets. For future work, how to incorporate symbol classifier result and correct segmentation error in MST-based parsing needs more research