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Tommi Jaakkola

Publications and source records attributed to Tommi Jaakkola.

138 records · Page 8Linked to original sources
arXiv2016

Structured Prediction: From Gaussian Perturbations to Linear-Time Principled Algorithms

Margin-based structured prediction commonly uses a maximum loss over all possible structured outputs \cite{Altun03,Collins04b,Taskar03}. In natural language processing, recent work \cite{Zhang14,Zhang15} has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution. This method is linear-time in the number of random structured outputs and trivially parallelizable. We study this family of loss functions in the PAC-Bayes framework under Gaussian perturbations \cite{McAllester07}. Under some technical conditions and up to statistical accuracy, we show that this family of loss functions produces a tighter upper bound of the Gibbs decoder distortion than commonly used methods. Thus, using the maximum loss over random structured outputs is a principled way of learning the parameter of structured prediction models. Besides explaining the experimental success of \cite{Zhang14,Zhang15}, our theoretical results show that more general techniques are possible.

stat.ML↗
arXiv2016

Semi-supervised Question Retrieval with Gated Convolutions

Question answering forums are rapidly growing in size with no effective automated ability to refer to and reuse answers already available for previous posted questions. In this paper, we develop a methodology for finding semantically related questions. The task is difficult since 1) key pieces of information are often buried in extraneous details in the question body and 2) available annotations on similar questions are scarce and fragmented. We design a recurrent and convolutional model (gated convolution) to effectively map questions to their semantic representations. The models are pre-trained within an encoder-decoder framework (from body to title) on the basis of the entire raw corpus, and fine-tuned discriminatively from limited annotations. Our evaluation demonstrates that our model yields substantial gains over a standard IR baseline and various neural network architectures (including CNNs, LSTMs and GRUs).

cs.CL↗
arXiv2015

Principal Differences Analysis: Interpretable Characterization of Differences between Distributions

We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite relaxation. In addition to deriving some convergence results, we illustrate how the approach may be applied to identify differences between cell populations in the somatosensory cortex and hippocampus as manifested by single cell RNA-seq. Our broader framework extends beyond the specific choice of Wasserstein divergence.

stat.ML↗
arXiv2015

On the Statistical Efficiency of $\ell_{1,p}$ Multi-Task Learning of Gaussian Graphical Models

In this paper, we present $\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lower bounds. We compare the statistical efficiency of multi-task learning versus that of single-task learning. For experiments, we use a block coordinate descent method that is provably convergent and generates a sequence of positive definite solutions. We provide experimental validation on synthetic data as well as on two publicly available real-world data sets, including functional magnetic resonance imaging and gene expression data.

cs.LG↗
arXiv2015

Steps Toward Deep Kernel Methods from Infinite Neural Networks

Contemporary deep neural networks exhibit impressive results on practical problems. These networks generalize well although their inherent capacity may extend significantly beyond the number of training examples. We analyze this behavior in the context of deep, infinite neural networks. We show that deep infinite layers are naturally aligned with Gaussian processes and kernel methods, and devise stochastic kernels that encode the information of these networks. We show that stability results apply despite the size, offering an explanation for their empirical success.

cs.LG↗
arXiv2015

Molding CNNs for text: non-linear, non-consecutive convolutions

The success of deep learning often derives from well-chosen operational building blocks. In this work, we revise the temporal convolution operation in CNNs to better adapt it to text processing. Instead of concatenating word representations, we appeal to tensor algebra and use low-rank n-gram tensors to directly exploit interactions between words already at the convolution stage. Moreover, we extend the n-gram convolution to non-consecutive words to recognize patterns with intervening words. Through a combination of low-rank tensors, and pattern weighting, we can efficiently evaluate the resulting convolution operation via dynamic programming. We test the resulting architecture on standard sentiment classification and news categorization tasks. Our model achieves state-of-the-art performance both in terms of accuracy and training speed. For instance, we obtain 51.2% accuracy on the fine-grained sentiment classification task.

cs.CL↗
arXiv2015

CRAFT: ClusteR-specific Assorted Feature selecTion

We present a framework for clustering with cluster-specific feature selection. The framework, CRAFT, is derived from asymptotic log posterior formulations of nonparametric MAP-based clustering models. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuitively appealing. The resulting algorithm is simple to implement and scales nicely, requires minimal parameter tuning, obviates the need to specify the number of clusters a priori, and compares favorably with other methods on real datasets.

cs.LG↗
arXiv2015

An Unsupervised Method for Uncovering Morphological Chains

Most state-of-the-art systems today produce morphological analysis based only on orthographic patterns. In contrast, we propose a model for unsupervised morphological analysis that integrates orthographic and semantic views of words. We model word formation in terms of morphological chains, from base words to the observed words, breaking the chains into parent-child relations. We use log-linear models with morpheme and word-level features to predict possible parents, including their modifications, for each word. The limited set of candidate parents for each word render contrastive estimation feasible. Our model consistently matches or outperforms five state-of-the-art systems on Arabic, English and Turkish.

cs.CL↗
arXiv2013

On Measure Concentration of Random Maximum A-Posteriori Perturbations

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased samples from the Gibbs distribution. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. More efficient algorithms use sequential sampling strategies based on the expected value of low dimensional MAP perturbations. This paper develops new measure concentration inequalities that bound the number of samples needed to estimate such expected values. Applying the general result to MAP perturbations can yield a more efficient algorithm to approximate sampling from the Gibbs distribution. The measure concentration result is of general interest and may be applicable to other areas involving expected estimations.

cs.LG↗
arXiv2013

On Sampling from the Gibbs Distribution with Random Maximum A-Posteriori Perturbations

In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low dimensional perturbations and solving the corresponding MAP assignments. Our approach also leads to new ways to derive lower bounds on partition functions. We demonstrate empirically that our method excels in the typical "high signal - high coupling" regime. The setting results in ragged energy landscapes that are challenging for alternative approaches to sampling and/or lower bounds.

cs.LG↗
arXiv2012

On the Partition Function and Random Maximum A-Posteriori Perturbations

In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the corresponding partition function. We show that our method excels in the typical "high signal - high coupling" regime that results in ragged energy landscapes difficult for alternative approaches.

cs.LG↗