21,962 research outputs found
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
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
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