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Register a new userRegularized Residual Quantization: a multi-layer sparse dictionary learning approach
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Added by
Sohrab Ferdowsi
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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The Residual Quantization (RQ) framework is revisited where the quantization distortion is being successively reduced in multi-layers. Inspired by the reverse-water-filling paradigm in rate-distortion theory, an efficient regularization on the variances of the codewords is introduced which allows to extend the RQ for very large numbers of layers and also for high dimensional data, without getting over-trained. The proposed Regularized Residual Quantization (RRQ) results in multi-layer dictionaries which are additionally sparse, thanks to the soft-thresholding nature of the regularization when applied to variance-decaying data which can arise from de-correlating transformations applied to correlated data. Furthermore, we also propose a general-purpose pre-processing for natural images which makes them suitable for such quantization. The RRQ framework is first tested on synthetic variance-decaying data to show its efficiency in quantization of high-dimensional data. Next, we use the RRQ in super-resolution of a database of facial images where it is shown that low-resolution facial images from the test set quantized with codebooks trained on high-resolution images from the training set show relevant high-frequency content when reconstructed with those codebooks.
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The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the computation of the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors -- or feature maps -- from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking: there are no pursuit algorithms that can serve this model exactly, nor are there conditions to guarantee a non-empty model. While one can easily obtain signals that approximately satisfy the ML-CSC constraints, it remains unclear how to simply sample from the model and, more importantly, how one can train the convolutional filters from real data. In this work, we propose a sound pursuit algorithm for the ML-CSC model by adopting a projection approach. We provide new and improved bounds on the stability of the solution of such pursuit and we analyze different practical alternatives to implement this in practice. We show that the training of the filters is essential to allow for non-trivial signals in the model, and we derive an online algorithm to learn the dictionaries from real data, effectively resulting in cascaded sparse convolutional layers. Last, but not least, we demonstrate the applicability of the ML-CSC model for several applications in an unsupervised setting, providing competitive results. Our work represents a bridge between matrix factorization, sparse dictionary learning and sparse auto-encoders, and we analyze these connections in detail.
In recent years, the attention mechanism contributes significantly to hypergraph based neural networks. However, these methods update the attention weights with the network propagating. That is to say, this type of attention mechanism is only suitable for deep learning-based methods while not applicable to the traditional machine learning approaches. In this paper, we propose a hypergraph based sparse attention mechanism to tackle this issue and embed it into dictionary learning. More specifically, we first construct a sparse attention hypergraph, asset attention weights to samples by employing the $ell_1$-norm sparse regularization to mine the high-order relationship among sample features. Then, we introduce the hypergraph Laplacian operator to preserve the local structure for subspace transformation in dictionary learning. Besides, we incorporate the discriminative information into the hypergraph as the guidance to aggregate samples. Unlike previous works, our method updates attention weights independently, does not rely on the deep network. We demonstrate the efficacy of our approach on four benchmark datasets.
In this paper, we develop a parameter estimation method for factorially parametrized models such as Factorial Gaussian Mixture Model and Factorial Hidden Markov Model. Our contributions are two-fold. First, we show that the emission matrix of the standard Factorial Model is unidentifiable even if the true assignment matrix is known. Secondly, we address the issue of identifiability by making a one component sharing assumption and derive a parameter learning algorithm for this case. Our approach is based on a dictionary learning problem of the form $X = O R$, where the goal is to learn the dictionary $O$ given the data matrix $X$. We argue that due to the specific structure of the activation matrix $R$ in the shared component factorial mixture model, and an incoherence assumption on the shared component, it is possible to extract the columns of the $O$ matrix without the need for alternating between the estimation of $O$ and $R$.
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are unknown, the corresponding optimization is inherently non-convex. This was a major challenge until recently, when provable algorithms for dictionary learning were proposed. Yet, these provide guarantees only on the recovery of the dictionary, without explicit recovery guarantees on the coefficients. Moreover, any estimation error in the dictionary adversely impacts the ability to successfully localize and estimate the coefficients. This potentially limits the utility of existing provable dictionary learning methods in applications where coefficient recovery is of interest. To this end, we develop NOODL: a simple Neurally plausible alternating Optimization-based Online Dictionary Learning algorithm, which recovers both the dictionary and coefficients exactly at a geometric rate, when initialized appropriately. Our algorithm, NOODL, is also scalable and amenable for large scale distributed implementations in neural architectures, by which we mean that it only involves simple linear and non-linear operations. Finally, we corroborate these theoretical results via experimental evaluation of the proposed algorithm with the current state-of-the-art techniques. Keywords: dictionary learning, provable dictionary learning, online dictionary learning, non-convex, sparse coding, support recovery, iterative hard thresholding, matrix factorization, neural architectures, neural networks, noodl, sparse representations, sparse signal processing.
Traditionally, quantization is designed to minimize the reconstruction error of a data source. When considering downstream classification tasks, other measures of distortion can be of interest; such as the 0-1 classification loss. Furthermore, it is desirable that the performance of these quantizers not deteriorate once they are deployed into production, as relearning the scheme online is not always possible. In this work, we present a class of algorithms that learn distributed quantization schemes for binary classification tasks. Our method performs well on unseen data, and is faster than previous methods proportional to a quadratic term of the dataset size. It works by regularizing the 0-1 loss with the reconstruction error. We present experiments on synthetic mixture and bivariate Gaussian data and compare training, testing, and generalization errors with a family of benchmark quantization schemes from the literature. Our method is called Regularized Classification-Aware Quantization.
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