DOCSLIB.ORG

Support Vector Machines for Dyadic Data

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Support Vector Machines for Dyadic Data Support Vector Machines for Dyadic Data Sepp Hochreiter and Klaus Obermayer Department of Electrical Engineering and Computer Science Technische UniversitÄat Berlin 10587 Berlin, Germany fhochreit,[email protected] Abstract We describe a new technique for the analysis of dyadic data, where two sets of objects (\row" and \column" objects) are characterized by a matrix of numerical values which describe their mutual relationships. The new technique, called \Potential Support Vector Machine" (P-SVM), is a large-margin method for the construction of classi¯ers and regression functions for the \column" objects. Contrary to standard support vec- tor machine approaches, the P-SVM minimizes a scale-invariant capacity measure and requires a new set of constraints. As a result, the P-SVM method leads to a usually sparse expansion of the classi¯cation and regres- sion functions in terms of the \row" rather than the \column" objects and can handle data and kernel matrices which are neither positive de¯nite nor square. We then describe two complementary regularization schemes. The ¯rst scheme improves generalization performance for classi¯cation and regression tasks, the second scheme leads to the selection of a small, informative set of \row" \support" objects and can be applied to feature selection. Benchmarks for classi¯cation, regression, and feature selection tasks are performed with toy data as well as with several real world data sets. The results show, that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as for true dyadic data sets. In addition, a theoretical justi¯cation is provided for the new approach. 1 Introduction Learning from examples in order to predict is one of the standard tasks in ma- chine learning. Many techniques have been developed to solve classi¯cation and regression problems, but by far most of them were speci¯cally designed for vectorial data. Vectorial data, where data objects are described by vectors of numbers which are treated as elements of a vector space, are very convenient, because of the structure imposed by the Euclidean metric. However, there are 1 datasets for which a vector-based description is inconvenient or simply wrong, and representations which consider relationships between objects, are more ap- propriate. A) a b c d B) a b c d e f g α 1.3 −2.2 −1.6 7.8 a 0.9 −0.1 −0.8 0.5 0.2 −0.5 −0.7 β −1.8 −1.1 7.2 2.3 b −0.1 0.9 0.6 0.3 −0.7 −0.6 0.3 χ 1.2 1.9 −2.9 −2.2 c −0.8 0.6 0.9 0.2 −0.6 0.6 0.5 δ 3.7 0.8 −0.6 2.5 d 0.5 0.3 0.2 0.9 0.7 0.1 0.3 ε 9.2 −9.4 −8.3 9.2 e 0.2 −0.7 −0.6 0.7 0.9 −0.9 −0.5 φ −7.7 8.6 −9.7 −7.4 f −0.5 −0.6 0.6 0.1 −0.9 0.9 0.9 γ −4.8 0.1 −1.2 0.9 g −0.7 0.3 0.5 0.3 −0.5 0.9 0.9 Figure 1: A) Dyadic data: Column objects a; b; : : : and row objects ®; ¯; : : : are represented by a matrix of numerical fvalues whicg h describe theirf mutualg relationships. B) Pairwise data: A special case of dyadic data, where row and column objects coincide. In the following we will study representations of data objects which are based on matrices. We consider \column" objects, which are the objects to be described, and \row" objects, which are the objects which serve for their description (cf. Fig. 1A). The whole dataset can then be represented using a rectangular matrix whose entries denote the relationships between the corre- sponding \row" and \column" objects. We will call representations of this form dyadic data (Hofmann and Puzicha, 1998; Li and Loken, 2002; Ho®, 2005). If \row" and \column" objects are from the same set (Fig. 1B), the representa- tion is usually called pairwise data, and the entries of the matrix can often be interpreted as the degree of similarity (or dissimilarity) between objects. Dyadic descriptions are more powerful than vector-based descriptions, as vectorial data can always be brought into dyadic form when required. This is often done for kernel-based classi¯ers or regression functions (SchÄolkopf and Smola, 2002; Vapnik, 1998), where a Gram matrix of mutual similarities is calculated before the predictor is learned. A similar procedure can also be used in cases where the \row" and \column" objects are from di®erent sets. If both of them are described by feature vectors, a matrix can be calculated by applying a kernel function to pairs of feature vectors, one vector describing a \row" and the other vector describing a \column" object. One example for this is the drug-gene matrix of Scherf et al. (2000), which was constructed as the product of a measured drug-sample and a measured sample-gene matrix and where the kernel function was a scalar product. 2 In many cases, however, dyadic descriptions emerge, because the matrix en- tries are measured directly. Pairwise data representations as a special case of dyadic data can be found for datasets where similarities or distances between objects are measured. Examples include sequential or biophysical similarities between proteins (Lipman and Pearson, 1985; Sigrist et al., 2002; Falquet et al., 2002), chromosome location or co-expression similarities between genes (Cre- mer et al., 1993; Lu et al., 1994; Heyer et al., 1999), co-citations of text docu- ments (White and McCain, 1989; Bayer et al., 1990; Ahlgren et al., 2003), or hyperlinks between web-pages (Kleinberg, 1999). In general, these measured matrices are symmetric but may not be positive de¯nite, and even if they are for the training set, they may not remain positive de¯nite, if new examples are included. Genuine dyadic data occur whenever two sets of objects are related. Examples are DNA microarray data (Southern, 1988; Lysov et al., 1988; Dr- manac et al., 1989; Bains and Smith, 1988), where the \column" objects are tissue samples, the \row" objects are genes, and every sample-gene pair is re- lated by the expression level of this particular gene in this particular sample. Other examples are web-documents, where both the \column" and \row" ob- jects are web-pages and \column" web-pages are described by either hyperlinks to or from the \row" objects, which give rise to a rectangular matrix1. Fur- ther examples include documents in a database described by word-frequencies (Salton, 1968) or molecules described by transferable atom equivalent (TAE) descriptors (Mazza et al., 2001). Traditionally, \row" objects have often been called \features" and \column" vectors of the dyadic data matrix have mostly been treated as \feature vectors" which live in an Euclidean vector space, even when the dyadic nature the data was made explicit, see (Graepel et al., 1999; Mangasarian, 1998) or the \feature map" method (SchÄolkopf and Smola, 2002). Di±culties, however, arise when features are heterogeneous, and \apples and oranges" must be compared. What theoretical arguments would, for example, justify, to treat the values of a set of TAE descriptors as coordinates of a vector in an Euclidean space? A \non-vectorial" approach to pairwise data is to interpret the data matrix as a Gram matrix and to apply support vector machines (SVM) for classi¯cation and regression if the data matrix is positive semide¯nite (Graepel et al., 1999). For inde¯nite (but symmetric) matrices two other non-vectorial approaches have been suggested (Graepel et al., 1999). In the ¯rst approach, the data matrix is projected into the subspace spanned by the eigenvectors with positive eigenval- ues. This is an approximation and one would expect good results only, if the absolute values of the negative eigenvalues are small compared to the dominant positive ones. In the second approach, directions of negative eigenvalues are processed by ipping the sign of these eigenvalues. All three approaches lead to positive semide¯nite matrices on the training set, but positive semide¯niteness is not assured, if a new test object must be included. An embedding approach was suggested by Herbrich et al. (1998) for antisymmetric matrices, but this was 1Note, that for pairwise data examples the linking matrix was symmetric because links were considered bidirectional. 3 speci¯cally designed for data sets, where the matrix entries denote preference relations between objects. In summary, no general and principled method exists to learn classi¯ers or regression functions for dyadic data. In order to avoid abovementioned shortcomings, we suggest to consider \col- umn" and \row" objects on an equal footing and interpret the matrix entries as the result of a kernel function or measurement kernel, which takes a \row" object, applies it to a \column" object, and outputs a number. It will turn out that mild conditions on this kernel su±ce to create a vector space endowed with a dot product into which the \row" and the \column" objects can be mapped. Using this mathematical argument as a justi¯cation, we show how to construct classi¯cation and regression functions in this vector space in analogy to the large margin based methods for learning perceptrons for vectorial data. Using an im- proved measure for model complexity and a new set of constraints which ensure a good performance on the training data, we arrive at a generally applicable method to learn predictors for dyadic data.
Load more

Recommended publications
  • Machine Learning: Unsupervised Methods Sepp Hochreiter Other Courses
    Machine Learning Unsupervised Methods Part 1 Sepp Hochreiter Institute of Bioinformatics Johannes Kepler University, Linz, Austria Course 3 ECTS 2 SWS VO (class) 1.5 ECTS 1 SWS UE (exercise) Basic Course of Master Bioinformatics Basic Course of Master Computer Science: Computational Engineering / Int. Syst. Class: Mo 15:30-17:00 (HS 18) Exercise: Mon 13:45-14:30 (S2 053) – group 1 Mon 14:30-15:15 (S2 053) – group 2+group 3 EXAMS: VO: 3 part exams UE: weekly homework (evaluated) Machine Learning: Unsupervised Methods Sepp Hochreiter Other Courses Lecture Lecturer 365,077 Machine Learning: Unsupervised Techniques VL Hochreiter Mon 15:30-17:00/HS 18 365,078 Machine Learning: Unsupervised Techniques – G1 UE Hochreiter Mon 13:45-14:30/S2 053 365,095 Machine Learning: Unsupervised Techniques – G2+G3 UE Hochreiter Mon 14:30-15:15/S2 053 365,041 Theoretical Concepts of Machine Learning VL Hochreiter Thu 15:30-17:00/S3 055 365,042 Theoretical Concepts of Machine Learning UE Hochreiter Thu 14:30-15:15/S3 055 365,081 Genome Analysis & Transcriptomics KV Regl Fri 8:30-11:00/S2 053 365,082 Structural Bioinformatics KV Regl Tue 8:30-11:00/HS 11 365,093 Deep Learning and Neural Networks KV Unterthiner Thu 10:15-11:45/MT 226 365,090 Special Topics on Bioinformatics (B/C/P/M): KV Klambauer block Population genetics 365,096 Special Topics on Bioinformatics (B/C/P/M): KV Klambauer block Artificial Intelligence in Life Sciences 365,079 Introduction to R KV Bodenhofer Wed 15:30-17:00/MT 127 365,067 Master's Seminar SE Hochreiter Mon 10:15-11:45/S3 318 365,080 Master's Thesis Seminar SS SE Hochreiter Mon 10:15-11:45/S3 318 365,091 Bachelor's Seminar SE Hochreiter - 365,019 Dissertantenseminar Informatik 3 SE Hochreiter Mon 10:15-11:45/S3 318 347,337 Bachelor Seminar Biological Chemistry JKU (incl.
    [Show full text]
  • Prof. Dr. Sepp Hochreiter
    Speaker: Univ.-Prof. Dr. Sepp Hochreiter Institute for Machine Learning & LIT AI Lab, Johannes Kepler University Linz, Austria Title: Deep Learning -- the Key to Enable Artificial Intelligence Abstract: Deep Learning has emerged as one of the most successful fields of machine learning and artificial intelligence with overwhelming success in industrial speech, language and vision benchmarks. Consequently it became the central field of research for IT giants like Google, Facebook, Microsoft, Baidu, and Amazon. Deep Learning is founded on novel neural network techniques, the recent availability of very fast computers, and massive data sets. In its core, Deep Learning discovers multiple levels of abstract representations of the input. The main obstacle to learning deep neural networks is the vanishing gradient problem. The vanishing gradient impedes credit assignment to the first layers of a deep network or early elements of a sequence, therefore limits model selection. Most major advances in Deep Learning can be related to avoiding the vanishing gradient like unsupervised stacking, ReLUs, residual networks, highway networks, and LSTM networks. Currently, LSTM recurrent neural networks exhibit overwhelmingly successes in different AI fields like speech, language, and text analysis. LSTM is used in Google’s translate and speech recognizer, Apple’s iOS 10, Facebooks translate, and Amazon’s Alexa. We use LSTM in collaboration with Zalando and Bayer, e.g. to analyze blogs and twitter news related to fashion and health. In the AUDI Deep Learning Center, which I am heading, and with NVIDIA we apply Deep Learning to advance autonomous driving. In collaboration with Infineon we use Deep Learning for perception tasks, e.g.
    [Show full text]
  • Evaluating Recurrent Neural Network Explanations
    Evaluating Recurrent Neural Network Explanations Leila Arras1, Ahmed Osman1, Klaus-Robert Muller¨ 2;3;4, and Wojciech Samek1 1Machine Learning Group, Fraunhofer Heinrich Hertz Institute, Berlin, Germany 2Machine Learning Group, Technische Universitat¨ Berlin, Berlin, Germany 3Department of Brain and Cognitive Engineering, Korea University, Seoul, Korea 4Max Planck Institute for Informatics, Saarbrucken,¨ Germany fleila.arras, [email protected] Abstract a particular decision, i.e., when the input is a se- quence of words: which words are determinant Recently, several methods have been proposed for the final decision? This information is crucial to explain the predictions of recurrent neu- ral networks (RNNs), in particular of LSTMs. to unmask “Clever Hans” predictors (Lapuschkin The goal of these methods is to understand the et al., 2019), and to allow for transparency of the network’s decisions by assigning to each in- decision-making process (EU-GDPR, 2016). put variable, e.g., a word, a relevance indicat- Early works on explaining neural network pre- ing to which extent it contributed to a partic- dictions include Baehrens et al.(2010); Zeiler and ular prediction. In previous works, some of Fergus(2014); Simonyan et al.(2014); Springen- these methods were not yet compared to one berg et al.(2015); Bach et al.(2015); Alain and another, or were evaluated only qualitatively. We close this gap by systematically and quan- Bengio(2017), with several works focusing on ex- titatively comparing these methods in differ- plaining the decisions of convolutional neural net- ent settings, namely (1) a toy arithmetic task works (CNNs) for image recognition. More re- which we use as a sanity check, (2) a five-class cently, this topic found a growing interest within sentiment prediction of movie reviews, and be- NLP, amongst others to explain the decisions of sides (3) we explore the usefulness of word general CNN classifiers (Arras et al., 2017a; Ja- relevances to build sentence-level representa- covi et al., 2018), and more particularly to explain tions.
    [Show full text]
  • Employing a Transformer Language Model for Information Retrieval and Document Classification
    DEGREE PROJECT IN THE FIELD OF TECHNOLOGY ENGINEERING PHYSICS AND THE MAIN FIELD OF STUDY COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020 Employing a Transformer Language Model for Information Retrieval and Document Classification Using OpenAI's generative pre-trained transformer, GPT-2 ANTON BJÖÖRN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Employing a Transformer Language Model for Information Retrieval and Document Classification ANTON BJÖÖRN Master in Machine Learning Date: July 11, 2020 Supervisor: Håkan Lane Examiner: Viggo Kann School of Electrical Engineering and Computer Science Host company: SSC - Swedish Space Corporation Company Supervisor: Jacob Ask Swedish title: Transformermodellers användbarhet inom informationssökning och dokumentklassificering iii Abstract As the information flow on the Internet keeps growing it becomes increasingly easy to miss important news which does not have a mass appeal. Combating this problem calls for increasingly sophisticated information retrieval meth- ods. Pre-trained transformer based language models have shown great gener- alization performance on many natural language processing tasks. This work investigates how well such a language model, Open AI’s General Pre-trained Transformer 2 model (GPT-2), generalizes to information retrieval and classi- fication of online news articles, written in English, with the purpose of compar- ing this approach with the more traditional method of Term Frequency-Inverse Document Frequency (TF-IDF) vectorization. The aim is to shed light on how useful state-of-the-art transformer based language models are for the construc- tion of personalized information retrieval systems. Using transfer learning the smallest version of GPT-2 is trained to rank and classify news articles achiev- ing similar results to the purely TF-IDF based approach.
    [Show full text]
  • An SMO Algorithm for the Potential Support Vector Machine
    LETTER Communicated by Terrence Sejnowski An SMO Algorithm for the Potential Support Vector Machine Tilman Knebel [email protected] Downloaded from http://direct.mit.edu/neco/article-pdf/20/1/271/817177/neco.2008.20.1.271.pdf by guest on 02 October 2021 Neural Information Processing Group, Fakultat¨ IV, Technische Universitat¨ Berlin, 10587 Berlin, Germany Sepp Hochreiter [email protected] Institute of Bioinformatics, Johannes Kepler University Linz, 4040 Linz, Austria Klaus Obermayer [email protected] Neural Information Processing Group, Fakultat¨ IV and Bernstein Center for Computational Neuroscience, Technische Universitat¨ Berlin, 10587 Berlin, Germany We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An efficient selection procedure for Lagrange multipliers is given, and two heuristics for improving the SMO procedure are described: block optimization and annealing of the regularization parameter . A comparison of the variants shows that the dual SMO, including block optimization and annealing, performs ef- ficiently in terms of computation time. In contrast to standard support vector machines (SVMs), the P-SVM is applicable to arbitrary dyadic data sets, but benchmarks are provided against libSVM’s -SVR and C-SVC implementations for problems that are also solvable by standard SVM methods. For those problems, computation time of the P-SVM is comparable to or somewhat higher than the standard SVM.
    [Show full text]
  • A Deep Learning Architecture for Conservative Dynamical Systems: Application to Rainfall-Runoff Modeling
    A Deep Learning Architecture for Conservative Dynamical Systems: Application to Rainfall-Runoff Modeling Grey Nearing Google Research [email protected] Frederik Kratzert LIT AI Lb & Institute for Machine Learning, Johannes Kepler University [email protected] Daniel Klotz LIT AI Lab & Institute for Machine Learning, Johannes Kepler University [email protected] Pieter-Jan Hoedt LIT AI Lab & Institute for Machine Learning, Johannes Kepler University [email protected] Günter Klambauer LIT AI Lab & Institute for Machine Learning, Johannes Kepler University [email protected] Sepp Hochreiter LIT AI Lab & Institute for Machine Learning, Johannes Kepler University [email protected] Hoshin Gupta Department of Hydrology and Atmospheric Sciences, University of Arizona [email protected] Sella Nevo Yossi Matias Google Research Google Research [email protected] [email protected] Abstract The most accurate and generalizable rainfall-runoff models produced by the hydro- logical sciences community to-date are based on deep learning, and in particular, on Long Short Term Memory networks (LSTMs). Although LSTMs have an explicit state space and gates that mimic input-state-output relationships, these models are not based on physical principles. We propose a deep learning architecture that is based on the LSTM and obeys conservation principles. The model is benchmarked on the mass-conservation problem of simulating streamflow. AI for Earth Sciences Workshop at NeurIPS 2020. 1 Introduction Due to computational challenges and to the increasing volume and variety of hydrologically-relevant Earth observation data, machine learning is particularly well suited to help provide efficient and reliable flood forecasts over large scales [12]. Hydrologists have known since the 1990’s that machine learning generally produces better streamflow estimates than either calibrated conceptual models or process-based models [7].
    [Show full text]
  • LONG SHORT TERM MEMORY NEURAL NETWORK for KEYBOARD GESTURE DECODING Ouais Alsharif, Tom Ouyang, Françoise Beaufays, Shumin Zhai
    LONG SHORT TERM MEMORY NEURAL NETWORK FOR KEYBOARD GESTURE DECODING Ouais Alsharif, Tom Ouyang, Franc¸oise Beaufays, Shumin Zhai, Thomas Breuel, Johan Schalkwyk Google ABSTRACT Gesture typing is an efficient input method for phones and tablets using continuous traces created by a pointed object (e.g., finger or stylus). Translating such continuous gestures into textual input is a challenging task as gesture inputs ex- hibit many features found in speech and handwriting such as high variability, co-articulation and elision. In this work, we address these challenges with a hybrid approach, combining a variant of recurrent networks, namely Long Short Term Memories [1] with conventional Finite State Transducer de- coding [2]. Results using our approach show considerable improvement relative to a baseline shape-matching-based system, amounting to 4% and 22% absolute improvement respectively for small and large lexicon decoding on real datasets and 2% on a synthetic large scale dataset. Index Terms— Long-short term memory, LSTM, gesture Fig. 1. An example keyboard with the word Today gestured. typing, keyboard decoder efficiency, accuracy and robustness. Efficiency is im- 1. INTRODUCTION portant because such solutions tend to run on mobile devices which permit a smaller footprint in terms of computation and The Word-Gesture Keyboard (WGK) [3], first published in memory. Accuracy and robustness are also crucial, as users early 2000s [4, 5] has become a popular text input method on are not expected to gesture type words with high accuracy. touchscreen mobile devices. In the last few years this new Since most users would be using a mobile device for input, keyboard input paradigm has appeared in many products in- it is highly likely that gestures would be offset, noisy or even cluding Google’s Android keyboard.
    [Show full text]
  • Are Pre-Trained Language Models Aware of Phrases?Simplebut Strong Baselinesfor Grammar Induction
    Published as a conference paper at ICLR 2020 ARE PRE-TRAINED LANGUAGE MODELS AWARE OF PHRASES?SIMPLE BUT STRONG BASELINES FOR GRAMMAR INDUCTION Taeuk Kim1, Jihun Choi1, Daniel Edmiston2 & Sang-goo Lee1 1Dept. of Computer Science and Engineering, Seoul National University, Seoul, Korea 2Dept. of Linguistics, University of Chicago, Chicago, IL, USA ftaeuk,jhchoi,[email protected], [email protected] ABSTRACT With the recent success and popularity of pre-trained language models (LMs) in natural language processing, there has been a rise in efforts to understand their in- ner workings. In line with such interest, we propose a novel method that assists us in investigating the extent to which pre-trained LMs capture the syntactic notion of constituency. Our method provides an effective way of extracting constituency trees from the pre-trained LMs without training. In addition, we report intriguing findings in the induced trees, including the fact that some pre-trained LMs outper- form other approaches in correctly demarcating adverb phrases in sentences. 1 INTRODUCTION Grammar induction, which is closely related to unsupervised parsing and latent tree learning, allows one to associate syntactic trees, i.e., constituency and dependency trees, with sentences. As gram- mar induction essentially assumes no supervision from gold-standard syntactic trees, the existing approaches for this task mainly rely on unsupervised objectives, such as language modeling (Shen et al., 2018b; 2019; Kim et al., 2019a;b) and cloze-style word prediction (Drozdov et al., 2019) to train their task-oriented models. On the other hand, there is a trend in the natural language pro- cessing (NLP) community of leveraging pre-trained language models (LMs), e.g., ELMo (Peters et al., 2018) and BERT (Devlin et al., 2019), as a means of acquiring contextualized word represen- tations.
    [Show full text]
  • Which Neural Net Architectures Give Rise to Exploding and Vanishing Gradients?
    Which Neural Net Architectures Give Rise to Exploding and Vanishing Gradients? Boris Hanin Department of Mathematics Texas A& M University College Station, TX, USA [email protected] Abstract We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network with ReLU activations. Our results show that the empirical variance of the squaresN of the entries in the input-output Jacobian of is exponential in a simple architecture-dependent constant β, given by the sumN of the reciprocals of the hidden layer widths. When β is large, the gradients computed by at initialization vary wildly. Our approach complements the mean field theory analysisN of random networks. From this point of view, we rigorously compute finite width corrections to the statistics of gradients at the edge of chaos. 1 Introduction A fundamental obstacle in training deep neural nets using gradient based optimization is the exploding and vanishing gradient problem (EVGP), which has attracted much attention (e.g. [BSF94, HBF+01, MM15, XXP17, PSG17, PSG18]) after first being studied by Hochreiter [Hoc91]. The EVGP occurs when the derivative of the loss in the SGD update @ W W λ L , (1) − @W is very large for some trainable parameters W and very small for others: @ L 0 or . @W ⇡ 1 This makes the increment in (1) either too small to be meaningful or too large to be precise. In practice, a number of ways of overcoming the EVGP have been proposed (see e.g. [Sch]). Let us mention three general approaches: (i) using architectures such as LSTMs [HS97], highway networks [SGS15], or ResNets [HZRS16] that are designed specifically to control gradients; (ii) precisely initializing weights (e.g.
    [Show full text]
  • Rectified Factor Networks for Biclustering
    Workshop track - ICLR 2016 RECTIFIED FACTOR NETWORKS FOR BICLUSTERING Djork-Arne´ Clevert, Thomas Unterthiner & Sepp Hochreiter Institute of Bioinformatics Johannes Kepler University, Linz, Austria fokko,unterthiner,[email protected] ABSTRACT Biclustering is evolving into one of the major tools for analyzing large datasets given as matrix of samples times features. Biclustering has been successfully ap- plied in life sciences, e.g. for drug design, in e-commerce, e.g. for internet retailing or recommender systems. FABIA is one of the most successful biclustering methods which excelled in dif- ferent projects and is used by companies like Janssen, Bayer, or Zalando. FABIA is a generative model that represents each bicluster by two sparse membership vec- tors: one for the samples and one for the features. However, FABIA is restricted to about 20 code units because of the high computational complexity of computing the posterior. Furthermore, code units are sometimes insufficiently decorrelated. Sample membership is difficult to determine because vectors do not have exact zero entries and can have both large positive and large negative values. We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of FABIA. RFNs efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means. RFN learning is a generalized alternating min- imization algorithm based on the posterior regularization method which enforces non-negative and normalized posterior means. Each code unit represents a biclus- ter, where samples for which the code unit is active belong to the bicluster and features that have activating weights to the code unit belong to the bicluster.
    [Show full text]
  • Blimp: the Benchmark of Linguistic Minimal Pairs for English
    BLiMP: The Benchmark of Linguistic Minimal Pairs for English Alex Warstadt1, Alicia Parrish1, Haokun Liu2, Anhad Mohananey2, Wei Peng2, Sheng-FuWang1, Samuel R. Bowman1,2,3 1Department of Linguistics 2Department of Computer Science 3Center for Data Science New York University New York University New York University {warstadt,alicia.v.parrish,haokunliu,anhad, weipeng,shengfu.wang,bowman}@nyu.edu Abstract of these studies uses a different set of metrics, and focuses on a small set of linguistic We introduce The Benchmark of Linguistic paradigms, severely limiting any possible big- Minimal Pairs (BLiMP),1 a challenge set for picture conclusions. evaluating the linguistic knowledge of lan- guage models (LMs) on major grammatical (1) a. ThecatsannoyTim.(grammatical) phenomena in English. BLiMP consists of b. *ThecatsannoysTim.(ungrammatical) 67 individual datasets, each containing 1,000 minimal pairs—that is, pairs of minimally dif- We introduce the Benchmark of Linguistic ferent sentences that contrast in grammatical Minimal Pairs (shortened to BLiMP), a linguis- acceptability and isolate specific phenomenon tically motivated benchmark for assessing the in syntax, morphology, or semantics. We gen- sensitivity of LMs to acceptability contrasts across erate the data according to linguist-crafted a wide range of English phenomena,covering both grammar templates, and human aggregate previously studied and novel contrasts. BLiMP agreement with the labels is 96.4%. We consists of 67 datasets automatically generated evaluate n-gram, LSTM, and Transformer from linguist-crafted grammar templates, each (GPT-2 and Transformer-XL) LMs by observ- containing 1,000 minimal pairs and organized ing whether they assign a higher probability to by phenomenon into 12 categories.
    [Show full text]
  • Revisit Long Short-Term Memory: an Optimization Perspective
    Revisit Long Short-Term Memory: An Optimization Perspective Qi Lyu, Jun Zhu State Key Laboratory of Intelligent Technology and Systems (LITS) Tsinghua National Laboratory for Information Science and Technology (TNList) Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China [email protected], [email protected] Abstract Long Short-Term Memory (LSTM) is a deep recurrent neural network archi- tecture with high computational complexity. Contrary to the standard practice to train LSTM online with stochastic gradient descent (SGD) methods, we pro- pose a matrix-based batch learning method for LSTM with full Backpropagation Through Time (BPTT). We further solve the state drifting issues as well as im- proving the overall performance for LSTM using revised activation functions for gates. With these changes, advanced optimization algorithms are applied to LSTM with long time dependency for the first time and show great advantages over SGD methods. We further demonstrate that large-scale LSTM training can be greatly accelerated with parallel computation architectures like CUDA and MapReduce. 1 Introduction Long Short-Term Memory (LSTM) [1] is a deep recurrent neural network (RNN) well-suited to learn from experiences to classify, process and predict time series when there are very long time lags of unknown size between important events. LSTM consists of LSTM blocks instead of (or in addition to) regular network units. A LSTM block may be described as a “smart” network unit that can remember a value for an arbitrary length of time. This is one of the main reasons why LSTM outperforms other sequence learning methods in numerous applications such as achieving the best known performance in speech recognition [2], and winning the ICDAR handwriting competition in 2009.
    [Show full text]