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eLife ◽  
2022 ◽  
Vol 11 ◽  
Author(s):  
Baohua Zhou ◽  
Zifan Li ◽  
Sunnie Kim ◽  
John Lafferty ◽  
Damon A Clark

Animals have evolved sophisticated visual circuits to solve a vital inference problem: detecting whether or not a visual signal corresponds to an object on a collision course. Such events are detected by specific circuits sensitive to visual looming, or objects increasing in size. Various computational models have been developed for these circuits, but how the collision-detection inference problem itself shapes the computational structures of these circuits remains unknown. Here, inspired by the distinctive structures of LPLC2 neurons in the visual system of Drosophila, we build anatomically-constrained shallow neural network models and train them to identify visual signals that correspond to impending collisions. Surprisingly, the optimization arrives at two distinct, opposing solutions, only one of which matches the actual dendritic weighting of LPLC2 neurons. Both solutions can solve the inference problem with high accuracy when the population size is large enough. The LPLC2-like solutions reproduces experimentally observed LPLC2 neuron responses for many stimuli, and reproduces canonical tuning of loom sensitive neurons, even though the models are never trained on neural data. Thus, LPLC2 neuron properties and tuning are predicted by optimizing an anatomically-constrained neural network to detect impending collisions. More generally, these results illustrate how optimizing inference tasks that are important for an animal's perceptual goals can reveal and explain computational properties of specific sensory neurons.


2022 ◽  
Author(s):  
Philipp Arras ◽  
Philipp Frank ◽  
Philipp Haim ◽  
Jakob Knollmüller ◽  
Reimar Leike ◽  
...  

AbstractThe immediate vicinity of an active supermassive black hole—with its event horizon, photon ring, accretion disk and relativistic jets—is an appropriate place to study physics under extreme conditions, particularly general relativity and magnetohydrodynamics. Observing the dynamics of such compact astrophysical objects provides insights into their inner workings, and the recent observations of M87* by the Event Horizon Telescope1–6 using very-long-baseline interferometry techniques allows us to investigate the dynamical processes of M87* on timescales of days. Compared with most radio interferometers, very-long-baseline interferometry networks typically have fewer antennas and low signal-to-noise ratios. Furthermore, the source is variable, prohibiting integration over time to improve signal-to-noise ratio. Here, we present an imaging algorithm7,8 that copes with the data scarcity and temporal evolution, while providing an uncertainty quantification. Our algorithm views the imaging task as a Bayesian inference problem of a time-varying brightness, exploits the correlation structure in time and reconstructs (2 + 1 + 1)-dimensional time-variable and spectrally resolved images. We apply this method to the Event Horizon Telescope observations of M87*9 and validate our approach on synthetic data. The time- and frequency-resolved reconstruction of M87* confirms variable structures on the emission ring and indicates extended and time-variable emission structures outside the ring itself.


Author(s):  
Diego Alberici ◽  
Francesco Camilli ◽  
Pierluigi Contucci ◽  
Emanuele Mingione

Abstract In this letter we present a finite temperature approach to a high-dimensional inference problem, the Wigner spiked model, with group dependent signal-to-noise ratios. For two classes of convex and non-convex network architectures the error in the reconstruction is described in terms of the solution of a mean-field spin-glass on the Nishimori line. In the cases studied the order parameters do not fluctuate and are the solution of finite dimensional variational problems. The deep architecture is optimized in order to confine the high temperature phase where reconstruction fails.


2021 ◽  
Author(s):  
Zhouji Liang ◽  
Florian Wellmann

Geological modeling has been widely adopted to investigate underground geometries. However, modeling processes inevitably have uncertainties due to scarcity of data, measurement errors, and simplification of modeling methods. Recent developments in geomodeling methods have introduced a Bayesian framework to constrain the model uncertainties by considering additional geophysical data into the modeling procedure. Markov chain Monte Carlo (MCMC) methods are normally used as tools to solve the Bayesian inference problem. To achieve a more efficient posterior exploration, advances inMCMC methods utilize derivative information. Hence, we introduce an approach to efficiently evaluate second-order derivatives in geological modeling and introduce a Hessian-informed MCMC method, the generalized preconditioned Crank-Nicolson (gpCN), as a tool to solve the 3D model-based gravity Bayesian inversion problem. The result is compared with two other widely applied MCMC methods, random walk Metropolis-Hasting and Hamiltonian Monte Carlo, on a synthetic three-layer geological model. Our experiment demonstrates that superior performance is achieved by the gpCN, which has the potential to be generalized to more complex models.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1652
Author(s):  
Margret Westerkamp ◽  
Igor Ovchinnikov ◽  
Philipp Frank ◽  
Torsten Enßlin

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.


2021 ◽  
pp. 096228022110417
Author(s):  
Andrea Simkus ◽  
Frank PA Coolen ◽  
Tahani Coolen-Maturi ◽  
Natasha A Karp ◽  
Claus Bendtsen

This paper investigates statistical reproducibility of the [Formula: see text]-test. We formulate reproducibility as a predictive inference problem and apply the nonparametric predictive inference method. Within our research framework, statistical reproducibility provides inference on the probability that the same test outcome would be reached, if the test were repeated under identical conditions. We present an nonparametric predictive inference algorithm to calculate the reproducibility of the [Formula: see text]-test and then use simulations to explore the reproducibility both under the null and alternative hypotheses. We then apply nonparametric predictive inference reproducibility to a real-life scenario of a preclinical experiment, which involves multiple pairwise comparisons of test groups, where different groups are given a different concentration of a drug. The aim of the experiment is to decide the concentration of the drug which is most effective. In both simulations and the application scenario, we study the relationship between reproducibility and two test statistics, the Cohen’s [Formula: see text] and the [Formula: see text]-value. We also compare the reproducibility of the [Formula: see text]-test with the reproducibility of the Wilcoxon Mann–Whitney test. Finally, we examine reproducibility for the final decision of choosing a particular dose in the multiple pairwise comparisons scenario. This paper presents advances on the topic of test reproducibility with relevance for tests used in pharmaceutical research.


2021 ◽  
Vol 2021 (12) ◽  
pp. 124004
Author(s):  
Parthe Pandit ◽  
Mojtaba Sahraee-Ardakan ◽  
Sundeep Rangan ◽  
Philip Schniter ◽  
Alyson K Fletcher

Abstract We consider the problem of estimating the input and hidden variables of a stochastic multi-layer neural network (NN) from an observation of the output. The hidden variables in each layer are represented as matrices with statistical interactions along both rows as well as columns. This problem applies to matrix imputation, signal recovery via deep generative prior models, multi-task and mixed regression, and learning certain classes of two-layer NNs. We extend a recently-developed algorithm—multi-layer vector approximate message passing, for this matrix-valued inference problem. It is shown that the performance of the proposed multi-layer matrix vector approximate message passing algorithm can be exactly predicted in a certain random large-system limit, where the dimensions N × d of the unknown quantities grow as N → ∞ with d fixed. In the two-layer neural-network learning problem, this scaling corresponds to the case where the number of input features as well as training samples grow to infinity but the number of hidden nodes stays fixed. The analysis enables a precise prediction of the parameter and test error of the learning.


2021 ◽  
Author(s):  
◽  
Tony Butler-Yeoman

<p>The ability to extract and model the meaning in data has been key to the success of modern machine learning. Typically, data reflects a combination of multiple sources that are mixed together. For example, photographs of people’s faces reflect the subject of the photograph, lighting conditions, angle, and background scene. It is therefore natural to wish to extract these multiple, largely independent, sources, which is known as disentangling in the literature. Additional benefits of disentangling arise from the fact that the data is then simpler, meaning that there are fewer free parameters, which reduces the curse of dimensionality and aids learning.  While there has been a lot of research into finding disentangled representations, it remains an open problem. This thesis considers a number of approaches to a particularly difficult version of this task: we wish to disentangle the complex causes of data in an entirely unsupervised setting. That is, given access only to unlabeled, entangled data, we search for algorithms that can identify the generative factors of that data, which we call causes. Further, we assume that causes can themselves be complex and require a high-dimensional representation.  We consider three approaches to this challenge: as an inference problem, as an extension of independent components analysis, and as a learning problem. Each method is motivated, described, and tested on a set of datasets build from entangled combinations of images, most commonly MNIST digits. Where the results fall short of disentangling, the reasons for this are dissected and analysed. The last method that we describe, which is based on combinations of autoencoders that learn to predict each other’s output, shows some promise on this extremely challenging problem.</p>


2021 ◽  
Author(s):  
◽  
Tony Butler-Yeoman

<p>The ability to extract and model the meaning in data has been key to the success of modern machine learning. Typically, data reflects a combination of multiple sources that are mixed together. For example, photographs of people’s faces reflect the subject of the photograph, lighting conditions, angle, and background scene. It is therefore natural to wish to extract these multiple, largely independent, sources, which is known as disentangling in the literature. Additional benefits of disentangling arise from the fact that the data is then simpler, meaning that there are fewer free parameters, which reduces the curse of dimensionality and aids learning.  While there has been a lot of research into finding disentangled representations, it remains an open problem. This thesis considers a number of approaches to a particularly difficult version of this task: we wish to disentangle the complex causes of data in an entirely unsupervised setting. That is, given access only to unlabeled, entangled data, we search for algorithms that can identify the generative factors of that data, which we call causes. Further, we assume that causes can themselves be complex and require a high-dimensional representation.  We consider three approaches to this challenge: as an inference problem, as an extension of independent components analysis, and as a learning problem. Each method is motivated, described, and tested on a set of datasets build from entangled combinations of images, most commonly MNIST digits. Where the results fall short of disentangling, the reasons for this are dissected and analysed. The last method that we describe, which is based on combinations of autoencoders that learn to predict each other’s output, shows some promise on this extremely challenging problem.</p>


2021 ◽  
Vol 5 (11) ◽  
pp. 301
Author(s):  
Chihiro Shibata ◽  
Naohiro Shichijo ◽  
Johei Matsuoka ◽  
Yuriko Takeshima ◽  
Jenn-Ming Yang ◽  
...  

Discontinuous carbon fiber-carbon matrix composites dispersed Si/SiC matrix composites have complicated microstructures that consist of four phases (C/C, Si, SiC, and C/SiC). The crack stability significantly depends on their geometrical arrangement. Nondestructive evaluation is needed to maintain the components in their safe condition. Although several nondestructive evaluation methods such as the Eddy current have been developed, any set of them is still inadequate in order to cover all of the scales and aspects that (C/C)/Si/SiC composites comprise. We propose a new method for nondestructive evaluation using vibration/resonance modes and deep learning. The assumed resolution is mm-order (approx. 1–10 mm), which laser vibrometers are generally capable of handling sufficiently. We utilize deep neural networks called convolutional auto-encoders for inferring damaged areas from vibration modes, which is a so-called inverse problem and infeasible to solve numerically in most cases. We solve this inference problem by training convolutional auto-encoders using vibration modes obtained from a non-damaged specimen with various frequencies as the dataset. Experimental results show that the proposed method successfully detects the damaged areas of validation specimens. One of the noteworthy points of this method is that we need only a few specimens for training deep neural networks, which generally require a large amount of data.


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