New bounds for circulant Johnson-Lindenstrauss embeddings

This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound $k=O(\epsilon^{-2}\log^{(1+\delta)} (n))$ for Gaussian circulant JL embeddings. Moreover, by using the Laplace transform technique (also called Bernstein's trick), we extend the result to subgaussian case. The bounds in this paper offer a small improvement over the current best bounds for Gaussian circulant JL embeddings for certain parameter regimes and are derived using more direct methods.Comment: 11 pages; accepted by Communications in Mathematical Science

LRMM: Learning to Recommend with Missing Modalities

Multimodal learning has shown promising performance in content-based recommendation due to the auxiliary user and item information of multiple modalities such as text and images. However, the problem of incomplete and missing modality is rarely explored and most existing methods fail in learning a recommendation model with missing or corrupted modalities. In this paper, we propose LRMM, a novel framework that mitigates not only the problem of missing modalities but also more generally the cold-start problem of recommender systems. We propose modality dropout (m-drop) and a multimodal sequential autoencoder (m-auto) to learn multimodal representations for complementing and imputing missing modalities. Extensive experiments on real-world Amazon data show that LRMM achieves state-of-the-art performance on rating prediction tasks. More importantly, LRMM is more robust to previous methods in alleviating data-sparsity and the cold-start problem.Comment: 11 pages, EMNLP 201

Controlling for heterogeneity in gravity models of trade and integration

This paper compares various specifications of the gravity model of trade as nested versions of a general specification that uses bilateral country-pair fixed effects to control for heterogeneity. For each specification, we show that the atheoretical restrictions used to obtain them from the general model are not supported statistically. Because the gravity model has become the "workhorse" baseline model for estimating the effects of international integration, this has important empirical implications. In particular, we show that, unless heterogeneity is accounted for correctly, gravity models can greatly overestimate the effects of integration on the volume of trade.International trade