Related papers: Shallow Representation is Deep: Learning Uncertain…
Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…
We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
Deep neural networks are in the limelight of machine learning with their excellent performance in many data-driven applications. However, they can lead to inaccurate predictions when queried in out-of-distribution data points, which can…
Robotic tasks such as manipulation with visual inputs require image features that capture the physical properties of the scene, e.g., the position and configuration of objects. Recently, it has been suggested to learn such features in an…
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…
Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging…
This paper introduces a novel direct approach to system identification of dynamic networks with missing data based on maximum likelihood estimation. Dynamic networks generally present a singular probability density function, which poses a…
The learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train…
Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…
The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…
A common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution…
We introduce random-kernel networks, a multilayer extension of random feature models where depth is created by deterministic kernel composition and randomness enters only in the outermost layer. We prove that deeper constructions can…
Few-shot image classification learns to recognize new categories from limited labelled data. Metric learning based approaches have been widely investigated, where a query sample is classified by finding the nearest prototype from the…
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…