3,829 research outputs found
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
PCA is one of the most widely used dimension reduction techniques. A related
easier problem is "subspace learning" or "subspace estimation". Given
relatively clean data, both are easily solved via singular value decomposition
(SVD). The problem of subspace learning or PCA in the presence of outliers is
called robust subspace learning or robust PCA (RPCA). For long data sequences,
if one tries to use a single lower dimensional subspace to represent the data,
the required subspace dimension may end up being quite large. For such data, a
better model is to assume that it lies in a low-dimensional subspace that can
change over time, albeit gradually. The problem of tracking such data (and the
subspaces) while being robust to outliers is called robust subspace tracking
(RST). This article provides a magazine-style overview of the entire field of
robust subspace learning and tracking. In particular solutions for three
problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition
(S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an
entire data vector is either an outlier or an inlier. The S+LR formulation
instead assumes that outliers occur on only a few data vector indices and hence
are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201
Causal Effect Inference with Deep Latent-Variable Models
Learning individual-level causal effects from observational data, such as
inferring the most effective medication for a specific patient, is a problem of
growing importance for policy makers. The most important aspect of inferring
causal effects from observational data is the handling of confounders, factors
that affect both an intervention and its outcome. A carefully designed
observational study attempts to measure all important confounders. However,
even if one does not have direct access to all confounders, there may exist
noisy and uncertain measurement of proxies for confounders. We build on recent
advances in latent variable modeling to simultaneously estimate the unknown
latent space summarizing the confounders and the causal effect. Our method is
based on Variational Autoencoders (VAE) which follow the causal structure of
inference with proxies. We show our method is significantly more robust than
existing methods, and matches the state-of-the-art on previous benchmarks
focused on individual treatment effects.Comment: Published as a conference paper at NIPS 201
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