Sparse Set Research Articles

Digital phenotyping of depression during pregnancy using self-report data.

Depression is a common pregnancy complication yet is often under-detected and, subsequently, undertreated. Data collected through mobile health tools may be used to support the identification of depression symptoms in pregnancy. An observational cohort study of 2062 pregnancies collected self-reports of patient history, mood, pregnancy-specific symptoms, and written language using a prenatal support app. These app inputs were used to model depression risk in subsequent 30- and 60-day periods throughout pregnancy. A selective inference lasso modeling approach examined the individual and additive value of each type of patient-reported app input. Depression models ranged in predictive power (AUC value of 0.64-0.83), depending on the type of inputs. The most predictive model included personal history, daily mood, and acute pregnancy-related symptoms (e.g., severe vomiting, cramping). Across models, daily mood was the strongest indicator of depression symptoms in the following month. Models that retained natural language inputs typically improved predictive accuracy and offered insight into the lived context associated with experiencing depression. Our findings are not generalizable beyond a digitally literate patient population that is self-motivated to report data during pregnancy. Simple patient reported data, including sparse language, shared directly via digital tools may support earlier depression symptom identification and a more nuanced understanding of depression context.

Survey Paper on Quantum Deep Reinforcement Learning for Robot Navigation Tasks

Abstract: Quantum deep reinforcement learning is an integration of the principles of quantum computing with deep reinforcement learning in an effort to advance robot navigation tasks. Due to the explosion of the state and action spaces, traditionally DRL methods are limited in scalability and efficiency. QDRL, however, uses quantum superposition and entanglement for more efficient processing of big amounts of information-it enables robots to learn optimal policies for navigating complex environments. We introduce here a new QDRL framework in which quantum neural networks encode policy functions and value estimates. We demonstrate how quantum circuits can take advantage of multi-dimensional state representations in order to strengthen the power of a robot in changing its environment over time. Benchmark experiments on navigation tasks reflect phenomenal acceleration in learning performance along with better decision-making accuracy compared to classical DRL methods. We then consider integrating such quantum algorithms, as Grover's search, to improve exploration strategies in sparse reward settings. The experiments show that QDRL speeds up convergence rates and provides robots with the possibility to react more rapidly to unexpected obstacles. It discusses new applications for quantum computing of autonomous systems, potentially applied to robotics, autonomous vehicles, and other environments which require complex decision making. Some lines of work in the future are optimization of the resources needed for quantum computers and hybrid architectures for the resolution of classical problems in navigation

Statistical Mapping of PFOA and PFOS in Groundwater throughout the Contiguous United States.

Per-and polyfluoroalkyl substances (PFAS) are synthetic chemicals that are increasingly being detected in groundwater. The negative health consequences associated with human exposure to PFAS make it essential to quantify the distribution of PFAS in groundwater systems. Mapping PFAS distributions is particularly challenging because a national patchwork of testing and reporting requirements has resulted in sparse and spatially biased data. In this analysis, an inhomogeneous Poisson process (IPP) modeling approach is adopted from ecological statistics to continuously map PFAS distributions in groundwater across the contiguous United States. The model is trained on a unique data set of 8910 PFAS groundwater measurements, using combined concentrations of two PFAS analytes. The IPP model predictions are compared with results from random forest models to highlight the robustness of this statistical modeling approach on sparse data sets. This analysis provides a new approach to not only map PFAS contamination in groundwater but also prioritize future sampling efforts.

Appearance-Based Gaze Estimation as a Benchmark for Eye Image Data Generation Methods

Data augmentation is commonly utilized to increase the size and diversity of training sets for deep learning tasks. In this study, we propose a novel application of an existing image generation approach in the domain of realistic eye images that leverages data collected from 40 subjects. This hybrid method combines the benefits of precise control over the image content provided by 3D rendering, while introducing the previously lacking photorealism and diversity into synthetic images through neural style transfer. We prove its general efficacy as a data augmentation tool for appearance-based gaze estimation when generated data are mixed with a sparse train set of real images. It improved the results for 39 out of 40 subjects, with an 11.22% mean and a 19.75% maximum decrease in gaze estimation error, achieving similar metrics for train and held-out subjects. We release our data repository of eye images with gaze labels used in this work for public access.

Robust and accurate visual geo-localization using prior map constructed by handheld LiDAR SLAM with camera image and terrestrial LiDAR point cloud

ABSTRACT Visual geo-localization using prior map of known environments has extensive applications in the fields such as self-driving, augmented reality and navigation. Currently, such prior maps are usually constructed by visual SLAM or SFM. However, the recent advances in LiDAR SLAM technology with RGB camera demonstrate great potential in efficient and accurate prior map construction and visual geo-localization. In this research, we developed a novel prior map construction approach which seamlessly integrates a handheld LiDAR SLAM system, a global LiDAR localization algorithm and a sparse set of terrestrial LiDAR scans as accurate control within a factor graph optimization framework. The developed LiDAR SLAM system augmented by terrestrial LiDAR scans achieves an improved mapping accuracy of 8 cm under GNSS-denied conditions in the areas over 50,000 m2 while the state-of-art FAST-LIO2 alone fails and produces a mapping error over 30 m. The results show that a competitive accuracy of visual geo-localization on a mobile phone using the constructed prior map is achieved (i.e. 60 and 76 cm in two tests respectively). Finally, this work also demonstrates a novel LiDAR point cloud fusion method that produces optimized and consistent coarse-to-fine 3D reconstruction in large and complex scenes.

A GAN-based stepwise full-field mechanical prediction model for architected metamaterials

The exploration of mechanical metamaterials, characterized by unique unit cells with significant macroscopic mechanical properties, is of crucial importance. Traditional methods relying on bioinspired structures lack broad design space and controllability to some extent, especially when practical requirements have no biological counterparts. Hence, there is a pressing need to advance methodologies for the expansive design of unit cells, catering to diverse practical demands. Inspired by architected material, a latent design paradigm gains prominence for its extensive possibilities and unique distribution. However, wide design space faces challenges in accurately assessing the deformation history and stress states of diverse units, requiring validation through experiments or simulations, and imposing efficiency constraints on design. Using patterns generated by a mimetic corrosion algorithm and computational simulations, a GAN-based machine learning surrogate model is constructed to predict the history of deformation and stress fields of architected unit cells with accuracy and efficiency, in which a stepwise mapping strategy is proposed to augment comprehension of mechanical information in image processing. In distinct cases covering both explored domains and several unexplored domains, the model achieves effective predictions, demonstrating the robustness and adaptability of the model in extrapolating predictions of both time domain and design space. The proposed method demonstrates efficacy, stability, and generalizability, pioneering a solution for the mechanical history prediction of architected metamaterials in a sparse data setting, thereby overcoming the limitations of the training set.

Sparse-Coding Variational Autoencoders.

The sparse coding model posits that the visual system has evolved to efficiently code natural stimuli using a sparse set of features from an overcomplete dictionary. The original sparse coding model suffered from two key limitations, however: (1) computing the neural response to an image patch required minimizing a nonlinear objective function via recurrent dynamics and (2) fitting relied on approximate inference methods that ignored uncertainty. Although subsequent work has developed several methods to overcome these obstacles, we propose a novel solution inspired by the variational autoencoder (VAE) framework. We introduce the sparse coding variational autoencoder (SVAE), which augments the sparse coding model with a probabilistic recognition model parameterized by a deep neural network. This recognition model provides a neurally plausible feedforward implementation for the mapping from image patches to neural activities and enables a principled method for fitting the sparse coding model to data via maximization of the evidence lower bound (ELBO). The SVAE differs from standard VAEs in three key respects: the latent representation is overcomplete (there are more latent dimensions than image pixels), the prior is sparse or heavy-tailed instead of gaussian, and the decoder network is a linear projection instead of a deep network. We fit the SVAE to natural image data under different assumed prior distributions and show that it obtains higher test performance than previous fitting methods. Finally, we examine the response properties of the recognition network and show that it captures important nonlinear properties of neurons in the early visual pathway.

Sharkovskii’s theorem and the limits of digital computers for the simulation of chaotic dynamical systems

Chaos is a unique paradigm in classical physics within which systems exhibit extreme sensitivity to the initial conditions. Thus, they need to be handled using probabilistic methods commonly based on ensembles. However, initial conditions generated by digital computers fall within the sparse set of discrete IEEE floating point numbers which have non-uniform distributions along the real axis. Therefore, there are many missing initial conditions whose absence might be expected to degrade the computed statistical properties of chaotic systems. The universality of this problem is enshrined in Sharkovskii’s theorem which is the simplest mathematical statement of the fact that no finite number representation of a chaotic dynamical system can account for all of its properties and shows that the precision of the representation limits the accuracy of the resulting digital behaviour.

Firth-Type Penalized Methods of the Modified Poisson and Least-Squares Regression Analyses for Binary Outcomes.

The modified Poisson and least-squares regression analyses for binary outcomes have been widely used as effective multivariable analysis methods to provide risk ratio and risk difference estimates in clinical and epidemiological studies. However, there is no certain evidence that assessed their operating characteristics under small and sparse data settings and no effective methods have been proposed for these regression analyses to address this issue. In this article, we show that the modified Poisson regression provides seriously biased estimates under small and sparse data settings. In addition, the modified least-squares regression provides unbiased estimates under these settings. We further show that the ordinary robust variance estimators for both of the methods have certain biases under situations that involve small or moderate sample sizes. To address these issues, we propose the Firth-type penalized methods for the modified Poisson and least-squares regressions. The adjustment methods lead to a more accurate and stable risk ratio estimator under small and sparse data settings, although the risk difference estimator is not invariant. In addition, to improve the inferences of the effect measures, we provide an improved robust variance estimator for these regression analyses. We conducted extensive simulation studies to assess the performances of the proposed methods under real-world conditions and found that the accuracies of the point and interval estimations were markedly improved by the proposed methods. We illustrate the effectiveness of these methods by applying them to a clinical study of epilepsy.

UWB RCS calculations of smooth targets via the multi-band beam summation method

We present an ultra-wide-band beam-summation (UWB-BS) algorithm for calculating the radar cross-section (RCS) of large smooth targets whose asymptotic numerical complexity is of O ( 1 ) . In this approach, the incident field is expanded into a sparse set of iso-diffracting Gaussian beams (ID-GB), tiling the phase space (PS) of beam origins and directions. The field of each ID-GB is then tracked through reflections from the scatterer until the beam emerges from the target zone and propagates to the far zone using a closed-form near-to-far (N2F) zone transformation, and finally, the beam contributions are aggregated to obtain the scattered field. The algorithm can accommodate a multi-octave frequency band by dividing it into octave-wide sub-bands and introducing a UWB-BS scheme such that the PS beam lattices in the higher sub-bands are obtained by spatial-spectral upsampling those of the lower bands. The PS summation of ID-GBs is a priori localized and involves a roughly constant relatively small number of contributing beams in all the sub-bands, leading to an O ( 1 ) (frequency-independent) asymptotic computational complexity. Furthermore, with the ID parametrization, the beam axes and their propagation and scattering parameters are frequency-independent and, therefore, need to be calculated only once and then reused for all frequencies, thus greatly reducing the numerical cost of computing the RCS at multiple frequencies. The paper describes all aspects of the algorithm, including the choice of the beam parameters for asymptotic error convergence and the utilization of localization for algorithmic efficacy.

Robust and Accurate Recognition of Carriage Linear Array Images for Train Fault Detection

Train fault detection often relies on comparing collected images with reference images, making accurate image type recognition crucial. Current systems use Automatic Equipment Identification (AEI) devices to recognize carriage numbers while capturing images, but damaged Radio Frequency (RF) tags or blurred characters can hinder this process. Carriage linear array images, with their high resolution, extreme aspect ratios, and local nonlinear distortions, present challenges for recognition algorithms. This paper proposes a method tailored for recognizing such images. We apply an object detection algorithm to locate key components, simplifying image recognition into a sparse point set alignment task. To handle local distortions, we introduce a weighted radial basis function (RBF) and maximize the similarity between Gaussian mixtures of point sets to determine RBF weights. Experiments show 100% recognition accuracy under nonlinear distortions up to 15%. The algorithm also performs robustly with detection errors and identifies categories from 79 image classes in 24 ms on an i7 CPU without GPU support. This method significantly reduces system costs and advances automatic exterior fault detection for trains.

The 4D Camera: An 87 kHz Direct Electron Detector for Scanning/Transmission Electron Microscopy

Abstract We describe the development, operation, and application of the 4D Camera—a 576 by 576 pixel active pixel sensor for scanning/transmission electron microscopy which operates at 87,000 Hz. The detector generates data at ∼480 Gbit/s which is captured by dedicated receiver computers with a parallelized software infrastructure that has been implemented to process the resulting 10–700 Gigabyte-sized raw datasets. The back illuminated detector provides the ability to detect single electron events at accelerating voltages from 30 to 300 kV. Through electron counting, the resulting sparse data sets are reduced in size by 10--300× compared to the raw data, and open-source sparsity-based processing algorithms offer rapid data analysis. The high frame rate allows for large and complex scanning diffraction experiments to be accomplished with typical scanning transmission electron microscopy scanning parameters.

Information-Theoretic Modeling of Categorical Spatiotemporal GIS Data.

An information-theoretic data mining method is employed to analyze categorical spatiotemporal Geographic Information System land use data. Reconstructability Analysis (RA) is a maximum-entropy-based data modeling methodology that works exclusively with discrete data such as those in the National Land Cover Database (NLCD). The NLCD is organized into a spatial (raster) grid and data are available in a consistent format for every five years from 2001 to 2021. An NLCD tool reports how much change occurred for each category of land use; for the study area examined, the most dynamic class is Evergreen Forest (EFO), so the presence or absence of EFO in 2021 was chosen as the dependent variable that our data modeling attempts to predict. RA predicts the outcome with approximately 80% accuracy using a sparse set of cells from a spacetime data cube consisting of neighboring lagged-time cells. When the predicting cells are all Shrubs and Grasses, there is a high probability for a 2021 state of EFO, while when the predicting cells are all EFO, there is a high probability that the 2021 state will not be EFO. These findings are interpreted as detecting forest clear-cut cycles that show up in the data and explain why this class is so dynamic. This study introduces a new approach to analyzing GIS categorical data and expands the range of applications that this entropy-based methodology can successfully model.

Minimal zero entropy subshifts can be unrestricted along any sparse set

Abstract We present a streamlined proof of a result essentially presented by the author in [Some counterexamples in topological dynamics. Ergod. Th. & Dynam. Sys.28(4) (2008), 1291–1322], namely that for every set $S = \{s_1, s_2, \ldots \} \subset \mathbb {N}$ of zero Banach density and finite set A, there exists a minimal zero-entropy subshift $(X, \sigma )$ so that for every sequence $u \in A^{\mathbb {Z}}$ , there is $x_u \in X$ with $x_u(s_n) = u(n)$ for all $n \in \mathbb {N}$ . Informally, minimal deterministic sequences can achieve completely arbitrary behavior upon restriction to a set of zero Banach density. As a corollary, this provides counterexamples to the polynomial Sarnak conjecture reported by Eisner [A polynomial version of Sarnak’s conjecture. C. R. Math. Acad. Sci. Paris353(7) (2015), 569–572] which are significantly more general than some recently provided by Kanigowski, Lemańczyk and Radziwiłł [Prime number theorem for analytic skew products. Ann. of Math. (2)199 (2024), 591–705] and by Lian and Shi [A counter-example for polynomial version of Sarnak’s conjecture. Adv. Math.384 (2021), Paper no. 107765] and shows that no similar result can hold under only the assumptions of minimality and zero entropy.

Discovering and Exploiting Sparse Rewards in a Learned Behavior Space.

Learning optimal policies in sparse rewards settings is difficult as the learning agent has little to no feedback on the quality of its actions. In these situations, a good strategy is to focus on exploration, hopefully leading to the discovery of a reward signal to improve on. A learning algorithm capable of dealing with this kind of setting has to be able to (1) explore possible agent behaviors and (2) exploit any possible discovered reward. Exploration algorithms have been proposed that require the definition of a low-dimension behavior space, in which the behavior generated by the agent's policy can be represented. The need to design a priori this space such that it is worth exploring is a major limitation of these algorithms. In this work, we introduce STAX, an algorithm designed to learn a behavior space on-the-fly and to explore it while optimizing any reward discovered (see Figure 1). It does so by separating the exploration and learning of the behavior space from the exploitation of the reward through an alternating two-step process. In the first step, STAX builds a repertoire of diverse policies while learning a low-dimensional representation of the high-dimensional observations generated during the policies evaluation. In the exploitation step, emitters optimize the performance of the discovered rewarding solutions. Experiments conducted on three different sparse reward environments show that STAX performs comparably to existing baselines while requiring much less prior information about the task as it autonomously builds the behavior space it explores.

Reward shaping via expectation maximization method

Reinforcement Learning (RL) has found widespread applications in various decision making tasks. However, it still faces challenges such as the deadly triad, slow convergence, and rewards drop, which limit its practical scope. This paper primarily addresses the issues of slow convergence and rewards drop observed during RL training. Our proposed solution involves a reward shaping method composed of two distinct components, each serving a specific purpose: speeding up training and enhancing stability. These two components are interconnected through hyper-parameters, and it has been observed that the choice of hyper-parameters plays a critical role in determining the final performance of the RL algorithm. To optimize these hyper-parameters effectively, we employ a discrete sampling technique to cover the value ranges of these parameters. This discrete sampling creates a sparse set of data points within the reward matrix. Subsequently, we introduce a fitting approach based on the Expectation Maximization (EM) algorithm to estimate the global maximum of the reward matrix along with the corresponding hyper-parameters combination. This EM method significantly reduces computational complexity. Our extensive experimental results across various RL environments have demonstrated the effectiveness of our proposed method. It successfully mitigates the issue of rewards drop while simultaneously accelerating the convergence speed of the RL algorithm.

An efficient method of predicting S-wave velocity using sparse Gaussian process regression for a tight sandstone reservoir

The shear wave (S-wave) velocity plays a crucial role in interpreting the lithology in seismic data, identifying fluids and predicting reservoirs. However, S-wave velocity is often unavailable due to the high cost of measurement and technical constraints. Conventional methods exhibit limitations that potentially impact the accuracy or efficiency on predicting S-wave velocity. Moreover, these methods always ignore the uncertainty quantification associated with the predicted results. This paper proposes a sparse Gaussian process regression (SGPR) method to predict the S-wave velocity in tight sandstone reservoirs. SGPR is a highly efficient regression technique that is based on the Gaussian process regression (GPR) method. In the SGPR method, inducing inputs are introduced to approximate the kernel matrix to decrease the computational complexity. A sparse set of inducing inputs and kernel hyperparameters are optimized through minimizing the Kullback-Leibler (KL) divergence between the exact posterior distribution and the approximate one. In this study, we select several types of logging data, which include porosity, water saturation, shale content, lithology and P-wave velocity, as the inputs for the SGPR method to predict S-wave velocity. To validate its effectiveness, we use the SGPR method to predict S-wave velocity in tight sandstone and compare the results with those from the GPR method, the bidirectional long short-term memory (BiLSTM) method and the Xu-White model. Additionally, we conduct cross-validation to demonstrate the robustness of the SGPR method. Our findings indicate that the SGPR method presents better performance and significant advantages about the accuracy and efficiency. Moreover, the SGPR method offers uncertainty quantification for the predicted S-wave velocity.

Fast radiance field reconstruction from sparse inputs

Neural Radiance Field (NeRF) has emerged as a powerful method in data-driven 3D reconstruction because of its simplicity and state-of-the-art performance. However, NeRF requires densely captured calibrated images and lengthy training and rendering time to realize high-resolution reconstruction. Thus, we propose a fast radiance field reconstruction method from a sparse set of images with silhouettes. Our approach integrates NeRF with Shape from Silhouette, a traditional 3D reconstruction method that uses silhouette information to fit the shape of an object. To combine NeRF’s implicit representation with Shape from Silhouette’s explicit representation, we propose a novel explicit–implicit radiance field representation consisting of voxel grids with confidence and feature embedding for geometry and a multilayer perceptron network to decode view-dependent color emission for appearance. We propose to make the reconstructed geometry compact by taking advantage of silhouette images, which can avoid the majority of artifacts in sparse input scenarios and speed up training and rendering. We also apply voxel dilating and pruning to refine the geometry prediction. In addition, we impose a total variation regularization on our model to encourage a smooth radiance field. Experiments on the DTU and the NeRF-Synthetic datasets show that our algorithm surpasses the existing baselines in terms of efficiency and accuracy.

Neural Novel Actor: Learning a Generalized Animatable Neural Representation for Human Actors.

We propose a new method for learning a generalized animatable neural human representation from a sparse set of multi-view imagery of multiple persons. The learned representation can be used to synthesize novel view images of an arbitrary person and further animate them with the user's pose control. While most existing methods can either generalize to new persons or synthesize animations with user control, none of them can achieve both at the same time. We attribute this accomplishment to the employment of a 3D proxy for a shared multi-person human model, and further the warping of the spaces of different poses to a shared canonical pose space, in which we learn a neural field and predict the person- and pose-dependent deformations, as well as appearance with the features extracted from input images. To cope with the complexity of the large variations in body shapes, poses, and clothing deformations, we design our neural human model with disentangled geometry and appearance. Furthermore, we utilize the image features both at the spatial point and on the surface points of the 3D proxy for predicting person- and pose-dependent properties. Experiments show that our method significantly outperforms the state-of-the-arts on both tasks.

HDhuman: High-Quality Human Novel-View Rendering From Sparse Views.

In this paper, we aim to address the challenge of novel view rendering of human performers that wear clothes with complex texture patterns using a sparse set of camera views. Although some recent works have achieved remarkable rendering quality on humans with relatively uniform textures using sparse views, the rendering quality remains limited when dealing with complex texture patterns as they are unable to recover the high-frequency geometry details that are observed in the input views. To this end, we propose HDhuman, which uses a human reconstruction network with a pixel-aligned spatial transformer and a rendering network with geometry-guided pixel-wise feature integration to achieve high-quality human reconstruction and rendering. The designed pixel-aligned spatial transformer calculates the correlations between the input views and generates human reconstruction results with high-frequency details. Based on the surface reconstruction results, the geometry-guided pixel-wise visibility reasoning provides guidance for multi-view feature integration, enabling the rendering network to render high-quality images at 2k resolution on novel views. Unlike previous neural rendering works that always need to train or fine-tune an independent network for a different scene, our method is a general framework that is able to generalize to novel subjects. Experiments show that our approach outperforms all the prior generic or specific methods on both synthetic data and real-world data. Source code and test data will be made publicly available for research purposes at http://cic.tju.edu.cn/faculty/likun/projects/HDhuman/index.html.