Dependence Maximizing Temporal Alignment via Squared-Loss Mutual Information

The goal of temporal alignment is to establish time correspondence between two sequences, which has many applications in a variety of areas such as speech processing, bioinformatics, computer vision, and computer graphics. In this paper, we propose a novel temporal alignment method called least-squares dynamic time warping (LSDTW). LSDTW finds an alignment that maximizes statistical dependency between sequences, measured by a squared-loss variant of mutual information. The benefit of this novel information-theoretic formulation is that LSDTW can align sequences with different lengths, different dimensionality, high non-linearity, and non-Gaussianity in a computationally efficient manner. In addition, model parameters such as an initial alignment matrix can be systematically optimized by cross-validation. We demonstrate the usefulness of LSDTW through experiments on synthetic and real-world Kinect action recognition datasets.Comment: 11 page

Deep Matching Autoencoders

Increasingly many real world tasks involve data in multiple modalities or views. This has motivated the development of many effective algorithms for learning a common latent space to relate multiple domains. However, most existing cross-view learning algorithms assume access to paired data for training. Their applicability is thus limited as the paired data assumption is often violated in practice: many tasks have only a small subset of data available with pairing annotation, or even no paired data at all. In this paper we introduce Deep Matching Autoencoders (DMAE), which learn a common latent space and pairing from unpaired multi-modal data. Specifically we formulate this as a cross-domain representation learning and object matching problem. We simultaneously optimise parameters of representation learning auto-encoders and the pairing of unpaired multi-modal data. This framework elegantly spans the full regime from fully supervised, semi-supervised, and unsupervised (no paired data) multi-modal learning. We show promising results in image captioning, and on a new task that is uniquely enabled by our methodology: unsupervised classifier learning.Comment: 10 page

Similarity of Neural Network Representations Revisited

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.Comment: ICML 201

Sufficient Component Analysis for Supervised Dimension Reduction

The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing methods. In our method, a solution is computed by iteratively performing dependence estimation and maximization: Dependence estimation is analytically carried out by recently-proposed least-squares mutual information (LSMI), and dependence maximization is also analytically carried out by utilizing the Epanechnikov kernel. Through large-scale experiments on real-world image classification and audio tagging problems, the proposed method is shown to compare favorably with existing dimension reduction approaches

Multiple-antenna fading coherent channels with arbitrary inputs: Characterization and optimization of the reliable information transmission rate

We investigate the constrained capacity of multiple-antenna fading coherent channels, where the receiver knows the channel state but the transmitter knows only the channel distribution, driven by arbitrary equiprobable discrete inputs in a regime of high signal-to-noise ratio (${\sf snr}$). In particular, we capitalize on intersections between information theory and estimation theory to conceive expansions to the average minimum-mean squared error (MMSE) and the average mutual information, which leads to an expansion of the constrained capacity, that capture well their behavior in the asymptotic regime of high ${\sf snr}$. We use the expansions to study the constrained capacity of various multiple-antenna fading coherent channels, including Rayleigh fading models, Ricean fading models and antenna-correlated models. The analysis unveils in detail the impact of the number of transmit and receive antennas, transmit and receive antenna correlation, line-of-sight components and the geometry of the signalling scheme on the reliable information transmission rate. We also use the expansions to design key system elements, such as power allocation and precoding schemes, as well as to design space-time signalling schemes for multiple-antenna fading coherent channels. Simulations results demonstrate that the expansions lead to very sharp designs

Global Sensitivity Analysis with Dependence Measures

Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which overcomes these insufficiencies. Our approach originates from the idea to compare the output distribution with its conditional counterpart when one of the input variables is fixed. We establish that this comparison yields previously proposed indices when it is performed with Csiszar f-divergences, as well as sensitivity indices which are well-known dependence measures between random variables. This leads us to investigate completely new sensitivity indices based on recent state-of-the-art dependence measures, such as distance correlation and the Hilbert-Schmidt independence criterion. We also emphasize the potential of feature selection techniques relying on such dependence measures as alternatives to screening in high dimension

Feature ranking for multi-label classification using Markov Networks

We propose a simple and efficient method for ranking features in multi-label classification. The method produces a ranking of features showing their relevance in predicting labels, which in turn allows to choose a final subset of features. The procedure is based on Markov Networks and allows to model the dependencies between labels and features in a direct way. In the first step we build a simple network using only labels and then we test how much adding a single feature affects the initial network. More specifically, in the first step we use the Ising model whereas the second step is based on the score statistic, which allows to test a significance of added features very quickly. The proposed approach does not require transformation of label space, gives interpretable results and allows for attractive visualization of dependency structure. We give a theoretical justification of the procedure by discussing some theoretical properties of the Ising model and the score statistic. We also discuss feature ranking procedure based on fitting Ising model using $l_1$ regularized logistic regressions. Numerical experiments show that the proposed methods outperform the conventional approaches on the considered artificial and real datasets

Probabilistic CCA with Implicit Distributions

Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear dependency. However, it is non-trivial to have an in-principle understanding of these variants due to their inherent restrictive assumption on the data and latent code distributions. Although some works have studied probabilistic interpretation for CCA, these models still require the explicit form of the distributions to achieve a tractable solution for the inference. In this work, we study probabilistic interpretation for CCA based on implicit distributions. We present Conditional Mutual Information (CMI) as a new criterion for CCA to consider both linear and nonlinear dependency for arbitrarily distributed data. To eliminate direct estimation for CMI, in which explicit form of the distributions is still required, we derive an objective which can provide an estimation for CMI with efficient inference methods. To facilitate Bayesian inference of multi-view analysis, we propose Adversarial CCA (ACCA), which achieves consistent encoding for multi-view data with the consistent constraint imposed on the marginalization of the implicit posteriors. Such a model would achieve superiority in the alignment of the multi-view data with implicit distributions. It is interesting to note that most of the existing CCA variants can be connected with our proposed CCA model by assigning specific form for the posterior and likelihood distributions. Extensive experiments on nonlinear correlation analysis and cross-view generation on benchmark and real-world datasets demonstrate the superiority of our model.Comment: 23 pages, 9 Figures; Keywords: Multi-view Learning, Nonlinear Dependency, Deep Generative model

Why Overfitting Isn't Always Bad: Retrofitting Cross-Lingual Word Embeddings to Dictionaries

Cross-lingual word embeddings (CLWE) are often evaluated on bilingual lexicon induction (BLI). Recent CLWE methods use linear projections, which underfit the training dictionary, to generalize on BLI. However, underfitting can hinder generalization to other downstream tasks that rely on words from the training dictionary. We address this limitation by retrofitting CLWE to the training dictionary, which pulls training translation pairs closer in the embedding space and overfits the training dictionary. This simple post-processing step often improves accuracy on two downstream tasks, despite lowering BLI test accuracy. We also retrofit to both the training dictionary and a synthetic dictionary induced from CLWE, which sometimes generalizes even better on downstream tasks. Our results confirm the importance of fully exploiting training dictionary in downstream tasks and explains why BLI is a flawed CLWE evaluation.Comment: ACL 202

Multi-view Alignment and Generation in CCA via Consistent Latent Encoding

Multi-view alignment, achieving one-to-one correspondence of multi-view inputs, is critical in many real-world multi-view applications, especially for cross-view data analysis problems. Recently, an increasing number of works study this alignment problem with Canonical Correlation Analysis (CCA). However, existing CCA models are prone to misalign the multiple views due to either the neglect of uncertainty or the inconsistent encoding of the multiple views. To tackle these two issues, this paper studies multi-view alignment from the Bayesian perspective. Delving into the impairments of inconsistent encodings, we propose to recover correspondence of the multi-view inputs by matching the marginalization of the joint distribution of multi-view random variables under different forms of factorization. To realize our design, we present Adversarial CCA (ACCA) which achieves consistent latent encodings by matching the marginalized latent encodings through the adversarial training paradigm. Our analysis based on conditional mutual information reveals that ACCA is flexible for handling implicit distributions. Extensive experiments on correlation analysis and cross-view generation under noisy input settings demonstrate the superiority of our model.Comment: 37 pages, 22 figure