Extractor-Based Time-Space Lower Bounds for Learning

A matrix $M: A \times X \rightarrow \{-1,1\}$ corresponds to the following learning problem: An unknown element $x \in X$ is chosen uniformly at random. A learner tries to learn $x$ from a stream of samples, $(a_1, b_1), (a_2, b_2) \ldots$, where for every $i$, $a_i \in A$ is chosen uniformly at random and $b_i = M(a_i,x)$. Assume that $k,\ell, r$ are such that any submatrix of $M$ of at least $2^{-k} \cdot |A|$ rows and at least $2^{-\ell} \cdot |X|$ columns, has a bias of at most $2^{-r}$. We show that any learning algorithm for the learning problem corresponding to $M$ requires either a memory of size at least $\Omega\left(k \cdot \ell \right)$, or at least $2^{\Omega(r)}$ samples. The result holds even if the learner has an exponentially small success probability (of $2^{-\Omega(r)}$). In particular, this shows that for a large class of learning problems, any learning algorithm requires either a memory of size at least $\Omega\left((\log |X|) \cdot (\log |A|)\right)$ or an exponential number of samples, achieving a tight $\Omega\left((\log |X|) \cdot (\log |A|)\right)$ lower bound on the size of the memory, rather than a bound of $\Omega\left(\min\left\{(\log |X|)^2,(\log |A|)^2\right\}\right)$ obtained in previous works [R17,MM17b]. Moreover, our result implies all previous memory-samples lower bounds, as well as a number of new applications. Our proof builds on [R17] that gave a general technique for proving memory-samples lower bounds

Gabor frames and deep scattering networks in audio processing

This paper introduces Gabor scattering, a feature extractor based on Gabor frames and Mallat's scattering transform. By using a simple signal model for audio signals specific properties of Gabor scattering are studied. It is shown that for each layer, specific invariances to certain signal characteristics occur. Furthermore, deformation stability of the coefficient vector generated by the feature extractor is derived by using a decoupling technique which exploits the contractivity of general scattering networks. Deformations are introduced as changes in spectral shape and frequency modulation. The theoretical results are illustrated by numerical examples and experiments. Numerical evidence is given by evaluation on a synthetic and a "real" data set, that the invariances encoded by the Gabor scattering transform lead to higher performance in comparison with just using Gabor transform, especially when few training samples are available.Comment: 26 pages, 8 figures, 4 tables. Repository for reproducibility: https://gitlab.com/hararticles/gs-gt . Keywords: machine learning; scattering transform; Gabor transform; deep learning; time-frequency analysis; CNN. Accepted and published after peer revisio

SizeNet: Weakly Supervised Learning of Visual Size and Fit in Fashion Images

Finding clothes that fit is a hot topic in the e-commerce fashion industry. Most approaches addressing this problem are based on statistical methods relying on historical data of articles purchased and returned to the store. Such approaches suffer from the cold start problem for the thousands of articles appearing on the shopping platforms every day, for which no prior purchase history is available. We propose to employ visual data to infer size and fit characteristics of fashion articles. We introduce SizeNet, a weakly-supervised teacher-student training framework that leverages the power of statistical models combined with the rich visual information from article images to learn visual cues for size and fit characteristics, capable of tackling the challenging cold start problem. Detailed experiments are performed on thousands of textile garments, including dresses, trousers, knitwear, tops, etc. from hundreds of different brands.Comment: IEEE Conference on Computer Vision and Pattern Recognition Workshop (CVPRW) 2019 Focus on Fashion and Subjective Search - Understanding Subjective Attributes of Data (FFSS-USAD