Diffuse optical tomography (DOT) is a severely ill-posed nonlinear inverse problem that seeks to estimate optical parameters from boundary measurements. In the Bayesian framework, the ill-posedness is diminished by incorporating {\em a priori} information of the optical parameters via the prior distribution. In case the target is sparse or sharp-edged, the common choice as the prior model are non-differentiable total variation and $\ell^1$ priors. Alternatively, one can hierarchically extend the variances of a Gaussian prior to obtain differentiable sparsity promoting priors. By doing this, the variances are treated as unknowns allowing the estimation to locate the discontinuities. In this work, we formulate hierarchical prior models for the nonlinear DOT inverse problem using exponential, standard gamma and inverse-gamma hyperpriors. Depending on the hyperprior and the hyperparameters, the hierarchical models promote different levels of sparsity and smoothness. To compute the MAP estimates, the previously proposed alternating algorithm is adapted to work with the nonlinear model. We then propose an approach based on the cumulative distribution function of the hyperpriors to select the hyperparameters. We evaluate the performance of the hyperpriors with numerical simulations and show that the hierarchical models can improve the localization, contrast and edge sharpness of the reconstructions.
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Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.
The computational demands of modern AI have spurred interest in optical neural networks (ONNs) which offer the potential benefits of increased speed and lower power consumption. However, current ONNs face various challenges,most significantly a limited calculation precision (typically around 4 bits) and the requirement for high-resolution signal format converters (digital-to-analogue conversions (DACs) and analogue-to-digital conversions (ADCs)). These challenges are inherent to their analog computing nature and pose significant obstacles in practical implementation. Here, we propose a digital-analog hybrid optical computing architecture for ONNs, which utilizes digital optical inputs in the form of binary words. By introducing the logic levels and decisions based on thresholding, the calculation precision can be significantly enhanced. The DACs for input data can be removed and the resolution of the ADCs can be greatly reduced. This can increase the operating speed at a high calculation precision and facilitate the compatibility with microelectronics. To validate our approach, we have fabricated a proof-of-concept photonic chip and built up a hybrid optical processor (HOP) system for neural network applications. We have demonstrated an unprecedented 16-bit calculation precision for high-definition image processing, with a pixel error rate (PER) as low as $1.8\times10^{-3}$ at an signal-to-noise ratio (SNR) of 18.2 dB. We have also implemented a convolutional neural network for handwritten digit recognition that shows the same accuracy as the one achieved by a desktop computer. The concept of the digital-analog hybrid optical computing architecture offers a methodology that could potentially be applied to various ONN implementations and may intrigue new research into efficient and accurate domain-specific optical computing architectures for neural networks.
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single-index structure, while the other is included linearly through the high-dimensional vector formed by its discretised observations. For this model, two new algorithms are presented for selecting relevant variables in the linear part and estimating the model. Both procedures utilise the functional origin of linear covariates. Finite sample experiments demonstrated the scope of application of both algorithms: the first method is a fast algorithm that provides a solution (without loss in predictive ability) for the significant computational time required by standard variable selection methods for estimating this model, and the second algorithm completes the set of relevant linear covariates provided by the first, thus improving its predictive efficiency. Some asymptotic results theoretically support both procedures. A real data application demonstrated the applicability of the presented methodology from a predictive perspective in terms of the interpretability of outputs and low computational cost.
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped with a quadratic regularization term. We provide sufficient conditions under which the proposed algorithm and its time-continuous limit converge exponentially fast to a desired time-implicit numerical solution. We show both theoretically and numerically that the convergence rate is independent of the grid size, which makes our method suitable for large-scale problems. The efficiency of our algorithm has been verified via a series of numerical examples conducted on various types of reaction-diffusion equations. The choice of optimal hyperparameters as well as comparisons with some classical root-finding algorithms are also discussed in the numerical section.
Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS "shadows" completely analogous to those in CS -- namely, point estimators calculated from the empirical frequencies of single measurements -- we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies -- differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying "shadow" umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.
We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.
We propose a neural network-based real-time volume rendering method for realistic and efficient rendering of volumetric media. The traditional volume rendering method uses path tracing to solve the radiation transfer equation, which requires a huge amount of calculation and cannot achieve real-time rendering. Therefore, this paper uses neural networks to simulate the iterative integration process of solving the radiative transfer equation to speed up the volume rendering of volume media. Specifically, the paper first performs data processing on the volume medium to generate a variety of sampling features, including density features, transmittance features and phase features. The hierarchical transmittance fields are fed into a 3D-CNN network to compute more important transmittance features. Secondly, the diffuse reflection sampling template and the highlight sampling template are used to layer the three types of sampling features into the network. This method can pay more attention to light scattering, highlights and shadows, and then select important channel features through the attention module. Finally, the scattering distribution of the center points of all sampling templates is predicted through the backbone neural network. This method can achieve realistic volumetric media rendering effects and greatly increase the rendering speed while maintaining rendering quality, which is of great significance for real-time rendering applications. Experimental results indicate that our method outperforms previous methods.
We present a novel combination of dynamic embedded topic models and change-point detection to explore diachronic change of lexical semantic modality in classical and early Christian Latin. We demonstrate several methods for finding and characterizing patterns in the output, and relating them to traditional scholarship in Comparative Literature and Classics. This simple approach to unsupervised models of semantic change can be applied to any suitable corpus, and we conclude with future directions and refinements aiming to allow noisier, less-curated materials to meet that threshold.
Serial, or sequential, fusion of multiple biometric matchers has been not thoroughly investigated so far. However, this approach exhibits some advantages with respect to the widely adopted parallel approaches. In this paper, we propose a novel theoretical framework for the assessment of performance of such systems, based on a previous work of the authors. Benefits in terms of performance are theoretically evaluated, as well as estimation errors in the model parameters computation. Model is analyzed from the viewpoint of its pros and cons, by mean of preliminary experiments performed on NIST Biometric Score Set 1.
Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing (SU) is a key technique that disentangles mixed pixels into constituent LULC types and their abundance fractions. While existing studies on Deep Learning (DL) for SU typically focus on single time-step hyperspectral (HS) or multispectral (MS) data, our work pioneers SU using MODIS MS time series, addressing missing data with end-to-end DL models. Our approach enhances a Long-Short Term Memory (LSTM)-based model by incorporating geographic, topographic (geo-topographic), and climatic ancillary information. Notably, our method eliminates the need for explicit endmember extraction, instead learning the input-output relationship between mixed spectra and LULC abundances through supervised learning. Experimental results demonstrate that integrating spectral-temporal input data with geo-topographic and climatic information significantly improves the estimation of LULC abundances in mixed pixels. To facilitate this study, we curated a novel labeled dataset for Andalusia (Spain) with monthly MODIS multispectral time series at 460m resolution for 2013. Named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU), this dataset provides pixel-level annotations of LULC abundances along with ancillary information. The dataset (//zenodo.org/records/7752348) and code (//github.com/jrodriguezortega/MSMTU) are available to the public.
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