Informed Proposal Monte Carlo

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach

What Will I Do Next? The Intention from Motion Experiment

In computer vision, video-based approaches have been widely explored for the early classification and the prediction of actions or activities. However, it remains unclear whether this modality (as compared to 3D kinematics) can still be reliable for the prediction of human intentions, defined as the overarching goal embedded in an action sequence. Since the same action can be performed with different intentions, this problem is more challenging but yet affordable as proved by quantitative cognitive studies which exploit the 3D kinematics acquired through motion capture systems. In this paper, we bridge cognitive and computer vision studies, by demonstrating the effectiveness of video-based approaches for the prediction of human intentions. Precisely, we propose Intention from Motion, a new paradigm where, without using any contextual information, we consider instantaneous grasping motor acts involving a bottle in order to forecast why the bottle itself has been reached (to pass it or to place in a box, or to pour or to drink the liquid inside). We process only the grasping onsets casting intention prediction as a classification framework. Leveraging on our multimodal acquisition (3D motion capture data and 2D optical videos), we compare the most commonly used 3D descriptors from cognitive studies with state-of-the-art video-based techniques. Since the two analyses achieve an equivalent performance, we demonstrate that computer vision tools are effective in capturing the kinematics and facing the cognitive problem of human intention prediction.Comment: 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshop

Excitation Backprop for RNNs

Deep models are state-of-the-art for many vision tasks including video action recognition and video captioning. Models are trained to caption or classify activity in videos, but little is known about the evidence used to make such decisions. Grounding decisions made by deep networks has been studied in spatial visual content, giving more insight into model predictions for images. However, such studies are relatively lacking for models of spatiotemporal visual content - videos. In this work, we devise a formulation that simultaneously grounds evidence in space and time, in a single pass, using top-down saliency. We visualize the spatiotemporal cues that contribute to a deep model's classification/captioning output using the model's internal representation. Based on these spatiotemporal cues, we are able to localize segments within a video that correspond with a specific action, or phrase from a caption, without explicitly optimizing/training for these tasks.Comment: CVPR 2018 Camera Ready Versio

Excitation Dropout: Encouraging Plasticity in Deep Neural Networks

We propose a guided dropout regularizer for deep networks based on the evidence of a network prediction defined as the firing of neurons in specific paths. In this work, we utilize the evidence at each neuron to determine the probability of dropout, rather than dropping out neurons uniformly at random as in standard dropout. In essence, we dropout with higher probability those neurons which contribute more to decision making at training time. This approach penalizes high saliency neurons that are most relevant for model prediction, i.e. those having stronger evidence. By dropping such high-saliency neurons, the network is forced to learn alternative paths in order to maintain loss minimization, resulting in a plasticity-like behavior, a characteristic of human brains too. We demonstrate better generalization ability, an increased utilization of network neurons, and a higher resilience to network compression using several metrics over four image/video recognition benchmarks

A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks of state-of-the-art algorithms, such as the Reduced Basis method, when addressing problems that show a slow decay in the Kolmogorov n-width. Our work is based on the use of deep autoencoders, which we employ for encoding and decoding a high fidelity approximation of the solution manifold. In order to fully exploit the approximation capabilities of neural networks, we consider a nonlinear version of the Kolmogorov n-width over which we base the concept of a minimal latent dimension. We show that this minimal dimension is intimately related to the topological properties of the solution manifold, and we provide some theoretical results with particular emphasis on second order elliptic PDEs. Finally, we report numerical experiments where we compare the proposed approach with classical POD-Galerkin reduced order models. In particular, we consider parametrized advection-diffusion PDEs, and we test the methodology in the presence of strong transport fields, singular terms and stochastic coefficients

HMCLab: a framework for solving diverse geophysical inverse problems using the Hamiltonian Monte Carlo method

The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a lack of a common platform for solving a range of different geophysical inverse problems and showing potential and pitfalls. We demonstrate a common framework to solve such inverse problems ranging from, e.g, earthquake source location to potential field data inversion and seismic tomography. Within this approach, we can provide probabilities related to certain properties or structures of the subsurface. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods, making the solution of tomographic problems ultimately feasible. These results can be obtained with "HMCLab", a tool for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyze the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community.Comment: 21 pages, 4 figure