High-dimensional Measurements Research Articles

Revealing the hierarchical structure of microbial communities

Measuring the dynamics of microbial communities results in high-dimensional measurements of taxa abundances over time and space, which is difficult to analyze due to complex changes in taxonomic compositions. This paper presents a new method to investigate and visualize the intrinsic hierarchical community structure implied by the measurements. The basic idea is to identify significant intersection sets, which can be seen as sub-communities making up the measured communities. Using the subset relationship, the intersection sets together with the measurements form a hierarchical structure visualized as a Hasse diagram. Chemical organization theory (COT) is used to relate the hierarchy of the sets of taxa to potential taxa interactions and to their potential dynamical persistence. The approach is demonstrated on a data set of community data obtained from bacterial 16S rRNA gene sequencing for samples collected monthly from four groundwater wells over a nearly 3-year period (n = 114) along a hillslope area. The significance of the hierarchies derived from the data is evaluated by showing that they significantly deviate from a random model. Furthermore, it is demonstrated how the hierarchy is related to temporal and spatial factors; and how the idea of a core microbiome can be extended to a set of interrelated core microbiomes. Together the results suggest that the approach can support developing models of taxa interactions in the future.

STAGED: A Spatial-Temporal Aware Graph Encoder–Decoder for Fault Diagnosis in Industrial Processes

Data-driven fault diagnosis for critical industrial processes has exhibited promising potential with massive operating data from the supervisory control and data acquisition system. However, automatically extracting the complicated interactions between measurements and subtly integrating it with temporal evolutions have not been fully considered. Besides, with the increasing complexity of industrial processes, accurately locating fault roots is of tremendous significance. In this article, we propose an unsupervised spatial-temporal aware graph encoder-decoder (STAGED) model for industrial fault diagnosis. Firstly, the high-dimensional measurements are constructed as a weighted graph to depict the complicated interactions. Then, the graph convolutional network, long short-term memory network and attention mechanism are applied to learn a comprehensive representation for multi-series. To enforce the model to better capture the temporal evolution, the dual decoder that performs reconstruction and prediction tasks simultaneously is adopted with a well-designed comprehensive loss function. By learning the spatial-temporal evolutions of datasets, faults can be diagnosed and located at a fine-grained level based on reconstruction deviations. To verify the performance of STAGED, experiments on Cranfield three-phase flow facility and secure water treatment datasets are implemented and the results indicate that it can provide insight into fault evolution and accurately diagnose faults.

Kernel functions embed into the autoencoder to identify the sparse models of nonlinear dynamics

Numerous researches have shown that there are three main challenges in data-driven model identification methods: high-dimensional measurements, system complexity and unknown underlying dynamical properties. For most nonlinear dynamics, the feature space defined by the coefficients of their control equations is sparse. Therefore, sparse regression methods are used to learn the sparse coefficients of the control equations of nonlinear dynamics. However, this method strongly depends on the appropriate selection of the sparse basis vectors. In this essay, the autoencoder is combined with the sparse regression method to simultaneously identify the sparse coordinate and a parsimonious, interpretable and generalizable model of the specified system. It also integrates kernel functions to map the intractable measurements in the hidden space of the autoencoder into a linearly distinguishable kernel space, which kernelizes the candidate function library of the sparse identification of nonlinear dynamics (SINDy) model as the sparse dictionaries. Therefore, the flexible representation of neural networks, the simplicity of sparse regression methods and the implicit non-linear representation of kernel functions are consolidated in this article. To inspect the reliability of the proposed model in this paper, a set of nonlinear dynamics formulated by ordinary differential equations (ODEs), second-order trigonometric functions and partial differential equations (PDEs) are utilized as test cases. And the comparisons between the proposed model and other model identification methods illustrate that the performance of the former is the best.

Unlimited One-Way Steering.

This work explores the asymmetry of quantum steering in a setup using high-dimensional entanglement. We construct entangled states with the following properties: (i)one party (Bob) can never steer the state of the other party (Alice), considering the most general measurements, and (ii)Alice can strongly steer the state of Bob, in the sense of demonstrating genuine high-dimensional steering. In other words, Alice can convince Bob that they share an entangled state of arbitrarily high Schmidt number, while Bob can never convince Alice that the state is even simply entangled. In this sense, one-way steering can become unlimited. A key result for our construction is a condition for the joint measurability of all high-dimensional measurements subjected to the combined effect of noise and loss, which is of independent interest.

Overview of High-Dimensional Measurement Error Regression Models

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained momentum due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of the objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several novel statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring in future research.

Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks

We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. In this setting, one optimizes over a measure restricted to be supported on the variety of an ideal generated by quadratic bilinear monomials. We show that this restriction enables an equivalent sparse reformulation of the GMP, where the single (high dimensional) measure variable is replaced by several (lower dimensional) measure variables supported on the maximal cliques of the graph corresponding to the quadratic bilinear constraints. We explore the resulting hierarchies of moment-based relaxations for the original dense formulation of GMP and this new, equivalent ideal-sparse reformulation, when applied to the problem of bounding nonnegative- and completely positive matrix factorization ranks. We show that the ideal-sparse hierarchies provide bounds that are at least as good (and often tighter) as those obtained from the dense hierarchy. This is in sharp contrast to the situation when exploiting correlative sparsity, as is most common in the literature, where the resulting bounds are weaker than the dense bounds. Moreover, while correlative sparsity requires the underlying graph to be chordal, no such assumption is needed for ideal-sparsity. Numerical results show that the ideal-sparse bounds are often tighter and much faster to compute than their dense analogs.

Application of the DMD Approach to High-Reynolds-Number Flow over an Idealized Ground Vehicle

This paper attempts to develop a Dynamic Mode Decomposition (DMD)-based Reduced Order Model (ROMs) that can quickly but accurately predict the forces and moments experienced by a road vehicle such that they be used by an on-board controller to determine the vehicle’s trajectory. DMD can linearize a large dataset of high-dimensional measurements by decomposing them into low-dimensional coherent structures and associated time dynamics. This ROM can then also be applied to predict the future state of the fluid flow. Existing literature on DMD is limited to low Reynolds number applications. This paper presents DMD analyses of the flow around an idealized road vehicle, called the Ahmed body, at a Reynolds number of 2.7×106. The high-dimensional dataset used in this paper was collected from a computational fluid dynamics (CFD) simulation performed using the Menter’s Shear Stress Transport (SST) turbulence model within the context of Improved Delayed Detached Eddy Simulations (IDDES). The DMD algorithm, as available in the literature, was found to suffer nonphysical dampening of the medium-to-high frequency modes. Enhancements to the existing algorithm were explored, and a modified DMD approach is presented in this paper, which includes: (a) a requirement of higher sampling rate to obtain a higher resolution of data, and (b) a custom filtration process to remove spurious modes. The modified DMD algorithm thus developed was applied to the high-Reynolds-number, separation-dominated flow past the idealized ground vehicle. The effectiveness of the modified algorithm was tested by comparing future predictions of force and moment coefficients as predicted by the DMD-based ROM to the reference CFD simulation data, and they were found to offer significant improvement.

Equivalence between simulability of high-dimensional measurements and high-dimensional steering

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels.

The regDIF R Package: Evaluating Complex Sources of Measurement Bias Using Regularized Differential Item Functioning

Measurement bias (MB), or differences in the measurement properties of a latent variable, is often evaluated for a single categorical background variable (e.g., gender). However, recent statistical advances now allow MB to be simultaneously evaluated across multiple continuous and categorical background variables (e.g., gender, age, culture). Regularization has also shown promising results for selecting true differential item functioning (DIF) effects in high-dimensional measurement models. Despite this progress, current software tools make it difficult for applied researchers to implement regularized DIF (Reg-DIF). The regDIF R package is thus introduced and shown to be a relatively fast and flexible implementation of the Reg-DIF method. Namely, regDIF allows for simultaneous modeling of multiple background variables, a variety of different item response functions, and multiple types of penalty methods, among other possibilities. This article demonstrates these features using simulated and real data and provides example code for researchers to use in their own work.

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis.

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

Long–short-term memory encoder–decoder with regularized hidden dynamics for fault detection in industrial processes

The ability of recurrent neural networks (RNN) to model nonlinear dynamics of high dimensional process data has enabled data-driven RNN-based fault detection algorithms. Previous studies have focused on detecting faults by identifying the discrepancies in data distribution between the faulty and normal data, as reflected in prediction errors generated by RNN models. However, in industrial processes, variations in data distribution can also result from changes in normal control setpoints and compensatory control adjustments in response to disturbances, making it hard to differentiate between normal and faulty conditions. This paper proposes a fault detection method utilizing a long short-term memory (LSTM) encoder–decoder structure with regularized hidden dynamics and reversible instance normalization (RevIN) to compactly represent high-dimensional measurements for effective monitoring. During training, the hidden states of the model are regularized to form a low-dimensional latent space representation of the original multivariate time series data. As a result, the prediction errors of the latent states can be used to monitor the abnormal dynamic variations, while the reconstruction errors of the measured variables are used to monitor the abnormal static variations. Furthermore, the proposed indices can reflect operating conditions, even when the distribution of test data changes, which helps distinguish faults from normal adjustments and disturbances that controllers can settle. Data from numerical simulation and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed fault detection method.

Abnormal structural and functional network topological properties associated with left prefrontal, parietal, and occipital cortices significantly predict childhood TBI-related attention deficits: A semi-supervised deep learning study.

Traumatic brain injury (TBI) is a major public health concern in children. Children with TBI have elevated risk in developing attention deficits. Existing studies have found that structural and functional alterations in multiple brain regions were linked to TBI-related attention deficits in children. Most of these existing studies have utilized conventional parametric models for group comparisons, which have limited capacity in dealing with large-scale and high dimensional neuroimaging measures that have unknown nonlinear relationships. Nevertheless, none of these existing findings have been successfully implemented to clinical practice for guiding diagnoses and interventions of TBI-related attention problems. Machine learning techniques, especially deep learning techniques, are able to handle the multi-dimensional and nonlinear information to generate more robust predictions. Therefore, the current research proposed to construct a deep learning model, semi-supervised autoencoder, to investigate the topological alterations in both structural and functional brain networks in children with TBI and their predictive power for post-TBI attention deficits. Functional magnetic resonance imaging data during sustained attention processing task and diffusion tensor imaging data from 110 subjects (55 children with TBI and 55 group-matched controls) were used to construct the functional and structural brain networks, respectively. A total of 60 topological properties were selected as brain features for building the model. The model was able to differentiate children with TBI and controls with an average accuracy of 82.86%. Functional and structural nodal topological properties associated with left frontal, inferior temporal, postcentral, and medial occipitotemporal regions served as the most important brain features for accurate classification of the two subject groups. Post hoc regression-based machine learning analyses in the whole study sample showed that among these most important neuroimaging features, those associated with left postcentral area, superior frontal region, and medial occipitotemporal regions had significant value for predicting the elevated inattentive and hyperactive/impulsive symptoms. Findings of this study suggested that deep learning techniques may have the potential to help identifying robust neurobiological markers for post-TBI attention deficits; and the left superior frontal, postcentral, and medial occipitotemporal regions may serve as reliable targets for diagnosis and interventions of TBI-related attention problems in children.

Physics-informed dynamic mode decomposition

In this work, we demonstrate how physical principles—such as symmetries, invariances and conservation laws—can be integrated into thedynamic mode decomposition(DMD). DMD is a widely used data analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD can produce models that are sensitive to noise, fail to generalize outside the training data and violate basic physical laws. Our physics-informed DMD (piDMD) optimization, which may be formulated as a Procrustes problem, restricts the family of admissible models to a matrix manifold that respects the physical structure of the system. We focus on five fundamental physical principles—conservation, self-adjointness, localization, causality and shift-equivariance—and derive several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations. With fewer degrees of freedom, piDMD models are less prone to overfitting, require less training data, and are often less computationally expensive to build than standard DMD models. We demonstrate piDMD on a range of problems, including energy-preserving fluid flow, the Schrödinger equation, solute advection-diffusion and three-dimensional transitional channel flow. In each case, piDMD outperforms standard DMD algorithms in metrics such as spectral identification, state prediction and estimation of optimal forcings and responses.

Deep phenotypic analysis of psychiatric features in genetically defined cohorts: application to XYY syndrome

BackgroundRecurrent gene dosage disorders impart substantial risk for psychopathology. Yet, understanding that risk is hampered by complex presentations that challenge classical diagnostic systems. Here, we present a suite of generalizable analytic approaches for parsing this clinical complexity, which we illustrate through application to XYY syndrome.MethodWe gathered high-dimensional measures of psychopathology in 64 XYY individuals and 60 XY controls, plus additional interviewer-based diagnostic data in the XYY group. We provide the first comprehensive diagnostic description of psychiatric morbidity in XYY syndrome and show how diagnostic morbidity relates to functioning, subthreshold symptoms, and ascertainment bias. We then map behavioral vulnerabilities and resilience across 67 behavioral dimensions before borrowing techniques from network science to resolve the mesoscale architecture of these dimensions and links to observable functional outcomes.ResultsCarriage of an extra Y-chromosome increases risk for diverse psychiatric diagnoses, with clinically impactful subthreshold symptomatology. Highest rates are seen for neurodevelopmental and affective disorders. A lower bound of < 25% of carriers are free of any diagnosis. Dimensional analysis of 67 scales details the profile of psychopathology in XYY, which survives control for ascertainment bias, specifies attentional and social domains as the most impacted, and refutes stigmatizing historical associations between XYY and violence. Network modeling compresses all measured symptom scales into 8 modules with dissociable links to cognitive ability, adaptive function, and caregiver strain. Hub modules offer efficient proxies for the full symptom network.ConclusionsThis study parses the complex behavioral phenotype of XYY syndrome by applying new and generalizable analytic approaches for analysis of deep-phenotypic psychiatric data in neurogenetic disorders.

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using 10^{16} signals. Moreover, the expected secret key rate was simulated to examine our protocol’s performance at various intrinsic error rate values, Q=(0.3%,0.6%,1%) caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about 10^{14} signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

A machine learning based approach towards high-dimensional mediation analysis

Mediation analysis is used to investigate the role of intermediate variables (mediators) that lie in the path between an exposure and an outcome variable. While significant research has focused on developing methods for assessing the influence of mediators on the exposure-outcome relationship, current approaches do not easily extend to settings where the mediator is high-dimensional. These situations are becoming increasingly common with the rapid increase of new applications measuring massive numbers of variables, including brain imaging, genomics, and metabolomics. In this work, we introduce a novel machine learning based method for identifying high dimensional mediators. The proposed algorithm iterates between using a machine learning model to map the high-dimensional mediators onto a lower-dimensional space, and using the predicted values as input in a standard three-variable mediation model. Hence, the machine learning model is trained to maximize the likelihood of the mediation model. Importantly, the proposed algorithm is agnostic to the machine learning model that is used, providing significant flexibility in the types of situations where it can be used. We illustrate the proposed methodology using data from two functional Magnetic Resonance Imaging (fMRI) studies. First, using data from a task-based fMRI study of thermal pain, we combine the proposed algorithm with a deep learning model to detect distributed, network-level brain patterns mediating the relationship between stimulus intensity (temperature) and reported pain at the single trial level. Second, using resting-state fMRI data from the Human Connectome Project, we combine the proposed algorithm with a connectome-based predictive modeling approach to determine brain functional connectivity measures that mediate the relationship between fluid intelligence and working memory accuracy. In both cases, our multivariate mediation model links exposure variables (thermal pain or fluid intelligence), high dimensional brain measures (single-trial brain activation maps or resting-state brain connectivity) and behavioral outcomes (pain report or working memory accuracy) into a single unified model. Using the proposed approach, we are able to identify brain-based measures that simultaneously encode the exposure variable and correlate with the behavioral outcome.

Thresholds and critical states for a stochastic predator–prey model with mixed functional responses

In this paper, we are committed to the study of thresholds (between persistence and extinction) for all the species in a stochastic predator–prey model, which takes both Beddington–DeAngelis and Holling-II functional responses. One interesting thing we find is that the ith Lyapunov exponent defined for an ergodic invariant measure may just happen to be the threshold for the ith species. Furthermore, we discuss the priority levels among multiple thresholds for the same species, which is a novel feature of this paper. A brief summary of priority level is that, Lyapunov exponent for a high-dimensional measure has higher priority than that of a low-dimensional measure. At the end of the paper, we analyze dynamic properties for some critical states.

Deep kernel learning of dynamical models from high-dimensional noisy data

This work proposes a stochastic variational deep kernel learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses high-dimensional measurements into low-dimensional state variables, and a latent dynamical model for the state variables that predicts the system evolution over time. The training of the proposed model is carried out in an unsupervised manner, i.e., not relying on labeled data. Our learning method is evaluated on the motion of a pendulum—a well studied baseline for nonlinear model identification and control with continuous states and control inputs—measured via high-dimensional noisy RGB images. Results show that the method can effectively denoise measurements, learn compact state representations and latent dynamical models, as well as identify and quantify modeling uncertainties.

Simulability of High-Dimensional Quantum Measurements.

We investigate the compression of quantum information with respect to a given set M of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from M and an arbitrary quantum state ρ are recovered exactly by first compressing ρ into a lower-dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set M is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative example involving mutually unbiased bases, and develop a method based on semidefinite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

A sparse additive model for high-dimensional interactions with an exposure variable

A conceptual paradigm for onset of a new disease is often considered to be the result of changes in entire biological networks whose states are affected by a complex interaction of genetic and environmental factors. However, when modeling a relevant phenotype as a function of high dimensional measurements, power to estimate interactions is low, the number of possible interactions could be enormous and their effects may be non-linear. A method called sail for detecting non-linear interactions with a key environmental or exposure variable in high-dimensional settings which respects the strong or weak heredity constraints is proposed. It is proven that asymptotically, sail possesses the oracle property, i.e., it performs as well as if the true model were known in advance. A computationally efficient fitting algorithm with automatic tuning parameter selection, which scales to high-dimensional datasets is proposed. Simulation results show that sail outperforms existing penalized regression methods in terms of prediction accuracy and support recovery when there are non-linear interactions with an exposure variable. sail is applied to detect non-linear interactions between genes and a prenatal psychosocial intervention program on cognitive performance in children at 4 years of age. Results show that individuals who are genetically predisposed to lower educational attainment are those who stand to benefit the most from the intervention. The proposed algorithms are implemented in an R package available on CRAN (https://cran.r-project.org/package=sail).