相关论文: Learning Set Functions that are Sparse in Non-Orth…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…

We consider fast, provably accurate algorithms for approximating functions on the $d$-dimensional torus, $f: \mathbb{ T }^d \rightarrow \mathbb{C}$, that are sparse (or compressible) in the Fourier basis. In particular, suppose that the…

We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in…

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…

The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…

Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the…

We extend the recent sparse Fourier transform algorithm of (Lawlor, Christlieb, and Wang, 2013) to the noisy setting, in which a signal of bandwidth N is given as a superposition of k << N frequencies and additive noise. We present two such…

A fundamental problem faced by object recognition systems is that objects and their features can appear in different locations, scales and orientations. Current deep learning methods attempt to achieve invariance to local translations via…

Non-uniformed 3D sparse data, e.g., point clouds or voxels in different spatial positions, make contribution to the task of 3D object detection in different ways. Existing basic components in sparse convolutional networks (Sparse CNNs)…

In a sparse representation based recognition scheme, it is critical to learn a desired dictionary, aiming both good representational power and discriminative performance. In this paper, we propose a new dictionary learning model for…

Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data,…

Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…

Learning from limited data is challenging because data scarcity leads to a poor generalization of the trained model. A classical global pooled representation will probably lose useful local information. Many few-shot learning methods have…

We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…