A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
DeepCAM learns convolutional dictionaries for image processing.
PerCDL learns personalized dictionaries for physiological signals combining global and local structures.
Convolutional sparse representations are a form of sparse representation with a structured, translation invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training images during the learning process, which results in very high memo…
Both the Dictionary Learning (DL) and Convolutional Neural Networks (CNN) are powerful image representation learning systems based on different mechanisms and principles, however whether we can seamlessly integrate them to improve the per-formance is noteworthy exploring. To address this issue, we propose a novel gener…
GPCDL uses Gaussian Processes to learn smooth templates from data.
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional inv…
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the convolutional sparse coding problem, the corresponding dictionary learning probl…
Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input…
Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computa…
In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a convolutional filter can be well approximated as a linear combination of a small set of dict…
We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for compressive sensing inversion based on convolutional factor analysis is develope…
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via dec…
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
We introduce a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a higher classification accuracy than AlexNet over the ImageNet 2012 dataset. The netwo…
This paper tackles spatio-temporal information preservation in machine learning.
Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated patterns can be positioned anywhere in signals or images, optimization techniques face…
Sparse dictionary learning (SDL) has become a popular method for adaptively identifying parsimonious representations of a dataset, a fundamental problem in machine learning and signal processing. While most work on SDL assumes a training dataset of independent and identically distributed samples, a variant known as con…
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 e…
A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of th…
Whereas CNNs have demonstrated immense progress in many vision problems, they suffer from a dependence on monumental amounts of labeled training data. On the other hand, dictionary learning does not scale to the size of problems that CNNs can handle, despite being very effective at low-level vision tasks such as denois…
We introduce a neural-network architecture, termed the constrained recurrent sparse autoencoder (CRsAE), that solves convolutional dictionary learning problems, thus establishing a link between dictionary learning and neural networks. Specifically, we leverage the interpretation of the alternating-minimization algorith…
We introduce a class of auto-encoder neural networks tailored to data from the natural exponential family (e.g., count data). The architectures are inspired by the problem of learning the filters in a convolutional generative model with sparsity constraints, often referred to as convolutional dictionary learning (CDL).…
UNHaP removes noise from physiological events using Hawkes processes.
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning probl…
Graph convolutional network (GCN) is generalization of convolutional neural network (CNN) to work with arbitrarily structured graphs. A binary adjacency matrix is commonly used in training a GCN. Recently, the attention mechanism allows the network to learn a dynamic and adaptive aggregation of the neighborhood. We pro…
Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduc…
Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal conv…
Study on Bayesian deep linear networks with multiple outputs and convolutional layers.
Bayesian method improves dictionary learning for complex problems.
It is well known that multiplication operations in convolutional layers of common CNNs consume a lot of time during inference stage. In this article we present a flexible method to decrease both computational complexity of convolutional layers in inference as well as amount of space to store them. The method is based o…
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networ…
Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations w…
A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding top-down image generation. A Bayesian support vector machine is linked to the top-…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown…
DeepAM optimizes deep neural networks for image super-resolution.
We present a two-stage approach for learning dictionaries for object classification tasks based on the principle of information maximization. The proposed method seeks a dictionary that is compact, discriminative, and generative. In the first stage, dictionary atoms are selected from an initial dictionary by maximizing…
This paper studies the convergence behaviour of dictionary learning via the Iterative Thresholding and K-residual Means (ITKrM) algorithm. On one hand it is proved that ITKrM is a contraction under much more relaxed conditions than previously necessary. On the other hand it is shown that there seem to exist stable fixe…
New MHSNs extract multiscale features from complex data for robust classification.
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to capture the global st…
Unlike common cancers, such as those of the prostate and breast, tumor grading in rare cancers is difficult and largely undefined because of small sample sizes, the sheer volume of time needed to undertake on such a task, and the inherent difficulty of extracting human-observed patterns. One of the most challenging exa…
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations implicitly assume circular boundary conditions and make it hard to fully exploit …
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 …
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning m…
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training …
A dictionary connects symplectic to contact geometry, with applications to complex and G-structures.
A parallel algorithm learns efficient Kronecker product dictionaries.
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …