Related papers: Multiscale analysis via pseudo-reversing and appli…
The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Multiscale feature hierarchies have been witnessed the success in the computer vision area. This further motivates researchers to design multiscale Transformer for natural language processing, mostly based on the self-attention mechanism.…
We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining…
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
Imaging and hyperspectral data analysis is central to progress across biology, medicine, chemistry, and physics. The core challenge lies in converting high-resolution or high-dimensional datasets into interpretable representations that…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features…
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…
Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…
Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data…
An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce…