Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor Methods

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical Gaussian mixtures, ICA, and sparse coding models. We provide tight concentration bounds for empirical moments through novel covering arguments. We analyze parameter recovery through a simple tensor power update algorithm. In the semi-supervised setting, we exploit the label or prior information to get a rough estimate of the model parameters, and then refine it using the tensor method on unlabeled samples. We establish that learning is possible when the number of components scales as $k=o(d^{p/2})$, where $d$ is the observed dimension, and $p$ is the order of the observed moment employed in the tensor method. Our concentration bound analysis also leads to minimax sample complexity for semi-supervised learning of spherical Gaussian mixtures. In the unsupervised setting, we use a simple initialization algorithm based on SVD of the tensor slices, and provide guarantees under the stricter condition that $k\le \beta d$ (where constant $\beta$ can be larger than $1$), where the tensor method recovers the components under a polynomial running time (and exponential in $\beta$). Our analysis establishes that a wide range of overcomplete latent variable models can be learned efficiently with low computational and sample complexity through tensor decomposition methods.Comment: Title change

Colorization as a Proxy Task for Visual Understanding

We investigate and improve self-supervision as a drop-in replacement for ImageNet pretraining, focusing on automatic colorization as the proxy task. Self-supervised training has been shown to be more promising for utilizing unlabeled data than other, traditional unsupervised learning methods. We build on this success and evaluate the ability of our self-supervised network in several contexts. On VOC segmentation and classification tasks, we present results that are state-of-the-art among methods not using ImageNet labels for pretraining representations. Moreover, we present the first in-depth analysis of self-supervision via colorization, concluding that formulation of the loss, training details and network architecture play important roles in its effectiveness. This investigation is further expanded by revisiting the ImageNet pretraining paradigm, asking questions such as: How much training data is needed? How many labels are needed? How much do features change when fine-tuned? We relate these questions back to self-supervision by showing that colorization provides a similarly powerful supervisory signal as various flavors of ImageNet pretraining.Comment: CVPR 2017 (Project page: http://people.cs.uchicago.edu/~larsson/color-proxy/

Slow and steady feature analysis: higher order temporal coherence in video

How can unlabeled video augment visual learning? Existing methods perform "slow" feature analysis, encouraging the representations of temporally close frames to exhibit only small differences. While this standard approach captures the fact that high-level visual signals change slowly over time, it fails to capture *how* the visual content changes. We propose to generalize slow feature analysis to "steady" feature analysis. The key idea is to impose a prior that higher order derivatives in the learned feature space must be small. To this end, we train a convolutional neural network with a regularizer on tuples of sequential frames from unlabeled video. It encourages feature changes over time to be smooth, i.e., similar to the most recent changes. Using five diverse datasets, including unlabeled YouTube and KITTI videos, we demonstrate our method's impact on object, scene, and action recognition tasks. We further show that our features learned from unlabeled video can even surpass a standard heavily supervised pretraining approach.Comment: in Computer Vision and Pattern Recognition (CVPR) 2016, Las Vegas, NV, June 201

Unsupervised learning of generative topic saliency for person re-identification

(c) 2014. The copyright of this document resides with its authors. It may be distributed unchanged freely in print or electronic forms.© 2014. The copyright of this document resides with its authors. Existing approaches to person re-identification (re-id) are dominated by supervised learning based methods which focus on learning optimal similarity distance metrics. However, supervised learning based models require a large number of manually labelled pairs of person images across every pair of camera views. This thus limits their ability to scale to large camera networks. To overcome this problem, this paper proposes a novel unsupervised re-id modelling approach by exploring generative probabilistic topic modelling. Given abundant unlabelled data, our topic model learns to simultaneously both (1) discover localised person foreground appearance saliency (salient image patches) that are more informative for re-id matching, and (2) remove busy background clutters surrounding a person. Extensive experiments are carried out to demonstrate that the proposed model outperforms existing unsupervised learning re-id methods with significantly simplified model complexity. In the meantime, it still retains comparable re-id accuracy when compared to the state-of-the-art supervised re-id methods but without any need for pair-wise labelled training data