HMM for discovering decision-making dynamics using reinforcement learning experiments

Major depressive disorder (MDD), a leading cause of years of life lived with disability, presents challenges in diagnosis and treatment due to its complex and heterogeneous nature. Emerging evidence indicates that reward processing abnormalities may serve as a behavioral marker for MDD. To measure reward processing, patients perform computer-based behavioral tasks that involve making choices or responding to stimulants that are associated with different outcomes, such as gains or losses in the laboratory. Reinforcement learning (RL) models are fitted to extract parameters that measure various aspects of reward processing (e.g. reward sensitivity) to characterize how patients make decisions in behavioral tasks. Recent findings suggest the inadequacy of characterizing reward learning solely based on a single RL model; instead, there may be a switching of decision-making processes between multiple strategies. An important scientific question is how the dynamics of strategies in decision-making affect the reward learning ability of individuals with MDD. Motivated by the probabilistic reward task within the Establishing Moderators and Biosignatures of Antidepressant Response in Clinical Care (EMBARC) study, we propose a novel RL-HMM (hidden Markov model) framework for analyzing reward-based decision-making. Our model accommodates decision-making strategy switching between two distinct approaches under an HMM: subjects making decisions based on the RL model or opting for random choices. We account for continuous RL state space and allow time-varying transition probabilities in the HMM. We introduce a computationally efficient Expectation-maximization (EM) algorithm for parameter estimation and use a nonparametric bootstrap for inference. Extensive simulation studies validate the finite-sample performance of our method. We apply our approach to the EMBARC study to show that MDD patients are less engaged in RL compared to the healthy controls, and engagement is associated with brain activities in the negative affect circuitry during an emotional conflict task.

rtestim: Time-varying reproduction number estimation with trend filtering

To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.

Cooling of a granular gas mixture in microgravity

Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than monodisperse ensembles but attracted comparably little attention so far. We present the observation and characterization of a mixture of rod-like particles with different sizes and masses in a drop tower experiment. Kinetic energy decay rates during granular cooling and collision rates were determined and Haff's law for homogeneous granular cooling was confirmed. Thereby, energy equipartition between the mixture components and between individual degrees of freedom is violated. Heavier particles keep a slightly higher average kinetic energy than lighter ones. Experimental results are supported by numerical simulations.

Predicting Seasonal Influenza Hospitalizations Using an Ensemble Super Learner: A Simulation Study

Accurate forecasts can inform response to outbreaks. Most efforts in influenza forecasting have focused on predicting influenza-like activity, with fewer on influenza-related hospitalizations. We conducted a simulation study to evaluate a super learner's predictions of 3 seasonal measures of influenza hospitalizations in the United States: peak hospitalization rate, peak hospitalization week, and cumulative hospitalization rate. We trained an ensemble machine learning algorithm on 15,000 simulated hospitalization curves and generated weekly predictions. We compared the performance of the ensemble (weighted combination of predictions from multiple prediction algorithms), the best-performing individual prediction algorithm, and a naive prediction (median of a simulated outcome distribution). Ensemble predictions performed similarly to the naive predictions early in the season but consistently improved as the season progressed for all prediction targets. The best-performing prediction algorithm in each week typically had similar predictive accuracy compared with the ensemble, but the specific prediction algorithm selected varied by week. An ensemble super learner improved predictions of influenza-related hospitalizations, relative to a naive prediction. Future work should examine the super learner's performance using additional empirical data on influenza-related predictors (e.g., influenza-like illness). The algorithm should also be tailored to produce prospective probabilistic forecasts of selected prediction targets.

BayesTME: An end-to-end method for multiscale spatial transcriptional profiling of the tissue microenvironment

Spatial variation in cellular phenotypes underlies heterogeneity in immune recognition and response to therapy in cancer and many other diseases. Spatial transcriptomics holds the potential to quantify such variation, but existing analysis methods are limited by their focus on individual tasks such as spot deconvolution. We present BayesTME, an end-to-end Bayesian method for analyzing spatial transcriptomics data. BayesTME unifies several previously distinct analysis goals under a single, holistic generative model. This unified approach enables BayesTME to deconvolve spots into cell phenotypes without any need for paired single-cell RNA-seq. BayesTME then goes beyond spot deconvolution to uncover spatial expression patterns among coordinated subsets of genes within phenotypes, which we term spatial transcriptional programs. BayesTME achieves state-of-the-art performance across myriad benchmarks. On human and zebrafish melanoma tissues, BayesTME identifies spatial transcriptional programs that capture fundamental biological phenomena such as bilateral symmetry and tumor-associated fibroblast and macrophage reprogramming. BayesTME is open source.

Gradient-based sparse principal component analysis with extensions to online learning

Sparse principal component analysis is an important technique for simultaneous dimensionality reduction and variable selection with high-dimensional data. In this work we combine the unique geometric structure of the sparse principal component analysis problem with recent advances in convex optimization to develop novel gradient-based sparse principal component analysis algorithms. These algorithms enjoy the same global convergence guarantee as the original alternating direction method of multipliers, and can be more efficiently implemented with the rich toolbox developed for gradient methods from the deep learning literature. Most notably, these gradient-based algorithms can be combined with stochastic gradient descent methods to produce efficient online sparse principal component analysis algorithms with provable numerical and statistical performance guarantees. The practical performance and usefulness of the new algorithms are demonstrated in various simulation studies. As an application, we show how the scalability and statistical accuracy of our method enable us to find interesting functional gene groups in high-dimensional RNA sequencing data.

Comprehensive hemocompatibility analysis on the application of diamond-like carbon to ePTFE artificial vascular prosthesis

The aim of this study was to obtain comprehensive data regarding the hemocompatibility of diamond-like carbon (DLC)-coated expanded polytetrafluoroethylene (ePTFE). DLC increased the hydrophilicity and smoothened the surface and fibrillar structure, respectively, of the ePTFE. DLC-coated ePTFE had more albumin and fibrinogen adsorption and less platelet adhesion than uncoated ePTFE. There were scarce red cell attachments in in vitro human and in vivo animal (rat and swine) whole blood contact tests in both DLC-coated and uncoated ePTFE. DLC-coated ePTFE had a similar but marginally thicker band movement than uncoated-ePTFE with SDS-PAGE after human whole blood contact test. In addition, survival studies of aortic graft replacement in rats (1.5 mm graft) and arteriovenous shunt in goats (4 mm graft) were performed to compare the patency and clot formation between DLC-coated and uncoated ePTFE grafts. Comparable patency was observed in both animal models. However, clots were observed in the luminal surface of the patent 1.5 mm DLC-coated ePTFE grafts, but not in that of uncoated ePTFE grafts. In conclusions, hemocompatibility of DLC-coated ePTFE was high and comparable to that of uncoated ePTFE. However, it failed to improve the hemocompatibility of 1.5 mm ePTFE graft probably because increased fibrinogen adsorption canceled the other beneficial effects of DLC.

Less is more: balancing noise reduction and data retention in fMRI with data-driven scrubbing

Functional MRI (fMRI) data may be contaminated by artifacts arising from a myriad of sources, including subject head motion, respiration, heartbeat, scanner drift, and thermal noise. These artifacts cause deviations from common distributional assumptions, introduce spatial and temporal outliers, and reduce the signal-to-noise ratio of the data-all of which can have negative consequences for the accuracy and power of downstream statistical analysis. Scrubbing is a technique for excluding fMRI volumes thought to be contaminated by artifacts and generally comes in two flavors. Motion scrubbing based on subject head motion-derived measures is popular but suffers from a number of drawbacks, among them the need to choose a threshold, a lack of generalizability to multiband acquisitions, and high rates of censoring of individual volumes and entire subjects. Alternatively, data-driven scrubbing methods like DVARS are based on observed noise in the processed fMRI timeseries and may avoid some of these issues. Here we propose "projection scrubbing", a novel data-driven scrubbing method based on a statistical outlier detection framework and strategic dimension reduction, including independent component analysis (ICA), to isolate artifactual variation. We undertake a comprehensive comparison of motion scrubbing with data-driven projection scrubbing and DVARS. We argue that an appropriate metric for the success of scrubbing is maximal data retention subject to reasonable performance on typical benchmarks such as the validity, reliability, and identifiability of functional connectivity. We find that stringent motion scrubbing yields worsened validity, worsened reliability, and produced small improvements to fingerprinting. Meanwhile, data-driven scrubbing methods tend to yield greater improvements to fingerprinting while not generally worsening validity or reliability. Importantly, however, data-driven scrubbing excludes a fraction of the number of volumes or entire sessions compared to motion scrubbing. The ability of data-driven fMRI scrubbing to improve data retention without negatively impacting the quality of downstream analysis has major implications for sample sizes in population neuroscience research.

Spatio-temporal clustering analysis using generalized lasso with an application to reveal the spread of Covid-19 cases in Japan

This study addressed the issue of determining multiple potential clusters with regularization approaches for the purpose of spatio-temporal clustering. The generalized lasso framework has flexibility to incorporate adjacencies between objects in the penalty matrix and to detect multiple clusters. A generalized lasso model with two L 1 penalties is proposed, which can be separated into two generalized lasso models: trend filtering of temporal effect and fused lasso of spatial effect for each time point. To select the tuning parameters, the approximate leave-one-out cross-validation (ALOCV) and generalized cross-validation (GCV) are considered. A simulation study is conducted to evaluate the proposed method compared to other approaches in different problems and structures of multiple clusters. The generalized lasso with ALOCV and GCV provided smaller MSE in estimating the temporal and spatial effect compared to unpenalized method, ridge, lasso, and generalized ridge. In temporal effects detection, the generalized lasso with ALOCV and GCV provided relatively smaller and more stable MSE than other methods, for different structure of true risk values. In spatial effects detection, the generalized lasso with ALOCV provided higher index of edges detection accuracy. The simulation also suggested using a common tuning parameter over all time points in spatial clustering. Finally, the proposed method was applied to the weekly Covid-19 data in Japan form March 21, 2020, to September 11, 2021, along with the interpretation of dynamic behavior of multiple clusters.

A robotic honeycomb for interaction with a honeybee colony

Robotic technologies have shown the capability to interact with living organisms and even to form integrated mixed societies composed of living and artificial agents. Biocompatible robots, incorporating sensing and actuation capable of generating and responding to relevant stimuli, can be a tool to study collective behaviors previously unattainable with traditional techniques. To investigate collective behaviors of the western honeybee (Apis mellifera), we designed a robotic system capable of observing and modulating the bee cluster using an array of thermal sensors and actuators. We initially integrated the system into a beehive populated with about 4000 bees for several months. The robotic system was able to observe the colony by continuously collecting spatiotemporal thermal profiles of the winter cluster. Furthermore, we found that our robotic device reliably modulated the superorganism's response to dynamic thermal stimulation, influencing its spatiotemporal reorganization. In addition, after identifying the thermal collapse of a colony, we used the robotic system in a "life-support" mode via its thermal actuators. Ultimately, we demonstrated a robotic device capable of autonomous closed-loop interaction with a cluster comprising thousands of individual bees. Such biohybrid societies open the door to investigation of collective behaviors that necessitate observing and interacting with the animals within a complete social context, as well as for potential applications in augmenting the survivability of these pollinators crucial to our ecosystems and our food supply.

Bayesian Trend Filtering via Proximal Markov Chain Monte Carlo

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations of proximal MCMC, however, require hyperparameters and regularization parameters to be prespecified. In this work, we extend the paradigm of proximal MCMC through introducing a novel new class of nondifferentiable priors called epigraph priors. As a proof of concept, we place trend filtering, which was originally a nonparametric regression problem, in a parametric setting to provide a posterior median fit along with credible intervals as measures of uncertainty. The key idea is to replace the nonsmooth term in the posterior density with its Moreau-Yosida envelope, which enables the application of the gradient-based MCMC sampler Hamiltonian Monte Carlo. The proposed method identifies the appropriate amount of smoothing in a data-driven way, thereby automating regularization parameter selection. Compared with conventional proximal MCMC methods, our method is mostly tuning free, achieving simultaneous calibration of the mean, scale and regularization parameters in a fully Bayesian framework.

More Powerful Selective Inference for the Graph Fused Lasso

The graph fused lasso-which includes as a special case the one-dimensional fused lasso-is widely used to reconstruct signals that are piecewise constant on a graph, meaning that nodes connected by an edge tend to have identical values. We consider testing for a difference in the means of two connected components estimated using the graph fused lasso. A naive procedure such as a z-test for a difference in means will not control the selective Type I error, since the hypothesis that we are testing is itself a function of the data. In this work, we propose a new test for this task that controls the selective Type I error, and conditions on less information than existing approaches, leading to substantially higher power. We illustrate our approach in simulation and on datasets of drug overdose death rates and teenage birth rates in the contiguous United States. Our approach yields more discoveries on both datasets. Supplementary materials for this article are available online.

Brain Regions Identified as Being Associated with Verbal Reasoning through the Use of Imaging Regression via Internal Variation

Brain-imaging data have been increasingly used to understand intellectual disabilities. Despite significant progress in biomedical research, the mechanisms for most of the intellectual disabilities remain unknown. Finding the underlying neurological mechanisms has been proved difficult, especially in children due to the rapid development of their brains. We investigate verbal reasoning, which is a reliable measure of individuals' general intellectual abilities, and develop a class of high-order imaging regression models to identify brain subregions which might be associated with this specific intellectual ability. A key novelty of our method is to take advantage of spatial brain structures, and specifically the piecewise smooth nature of most imaging coefficients in the form of high-order tensors. Our approach provides an effective and urgently needed method for identifying brain subregions potentially underlying certain intellectual disabilities. The idea behind our approach is a carefully constructed concept called Internal Variation (IV). The IV employs tensor decomposition and provides a computationally feasible substitution for Total Variation (TV), which has been considered in the literature to deal with similar problems but is problematic in high order tensor regression. Before applying our method to analyze the real data, we conduct comprehensive simulation studies to demonstrate the validity of our method in imaging signal identification. Then, we present our results from the analysis of a dataset based on the Philadelphia Neurodevelopmental Cohort for which we preprocessed the data including re-orienting, bias-field correcting, extracting, normalizing and registering the magnetic resonance images from 978 individuals. Our analysis identified a subregion across the cingulate cortex and the corpus callosum as being associated with individuals' verbal reasoning ability, which, to the best of our knowledge, is a novel region that has not been reported in the literature. This finding is useful in further investigation of functional mechansims for verbal reasoning.

Risk bounds for quantile trend filtering

We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to logarithmic factors, when the $(r-1)$th discrete derivative of the true vector of quantiles belongs to the class of bounded-variation signals. Moreover, we show that if the true vector of quantiles is a discrete spline with a few polynomial pieces, then both versions attain a near-parametric rate of convergence. Corresponding results for the usual trend-filtering estimators are known to hold only when the errors are sub-Gaussian. In contrast, our risk bounds are shown to hold under minimal assumptions on the error variables. In particular, no moment assumptions are needed and our results hold under heavy-tailed errors. Our proof techniques are general, and thus can potentially be used to study other nonparametric quantile regression methods. To illustrate this generality, we employ our proof techniques to obtain new results for multivariate quantile total-variation denoising and high-dimensional quantile linear regression.

Nonparametric coalescent inference of mutation spectrum history and demography

As populations boom and bust, the accumulation of genetic diversity is modulated, encoding histories of living populations in present-day variation. Many methods exist to decode these histories, and all must make strong model assumptions. It is typical to assume that mutations accumulate uniformly across the genome at a constant rate that does not vary between closely related populations. However, recent work shows that mutational processes in human and great ape populations vary across genomic regions and evolve over time. This perturbs the mutation spectrum (relative mutation rates in different local nucleotide contexts). Here, we develop theoretical tools in the framework of Kingman's coalescent to accommodate mutation spectrum dynamics. We present mutation spectrum history inference (mushi), a method to perform nonparametric inference of demographic and mutation spectrum histories from allele frequency data. We use mushi to reconstruct trajectories of effective population size and mutation spectrum divergence between human populations, identify mutation signatures and their dynamics in different human populations, and calibrate the timing of a previously reported mutational pulse in the ancestors of Europeans. We show that mutation spectrum histories can be placed in a well-studied theoretical setting and rigorously inferred from genomic variation data, like other features of evolutionary history.

Detecting multiple generalized change-points by isolating single ones

We introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with are changes in the mean of a piecewise-constant signal and changes, continuous or not, in the linear trend. The number of change-points can increase with the sample size. Our method is based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point. This isolation enhances ID's accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. In ID, model selection is carried out via thresholding, or an information criterion, or SDLL, or a hybrid involving the former two. The hybrid model selection leads to a general method with very good practical performance and minimal parameter choice. In the scenarios tested, ID is at least as accurate as the state-of-the-art methods; most of the times it outperforms them. ID is implemented in the R packages IDetect and breakfast, available from CRAN.

SUPPLEMENTARY INFORMATION

The online version supplementary material available at 10.1007/s00184-021-00821-6.

Dose-response modeling in high-throughput cancer drug screenings: an end-to-end approach

Personalized cancer treatments based on the molecular profile of a patient's tumor are an emerging and exciting class of treatments in oncology. As genomic tumor profiling is becoming more common, targeted treatments for specific molecular alterations are gaining traction. To discover new potential therapeutics that may apply to broad classes of tumors matching some molecular pattern, experimentalists and pharmacologists rely on high-throughput, in vitro screens of many compounds against many different cell lines. We propose a hierarchical Bayesian model of how cancer cell lines respond to drugs in these experiments and develop a method for fitting the model to real-world high-throughput screening data. Through a case study, the model is shown to capture nontrivial associations between molecular features and drug response, such as requiring both wild type TP53 and overexpression of MDM2 to be sensitive to Nutlin-3(a). In quantitative benchmarks, the model outperforms a standard approach in biology, with $\approx20\%$ lower predictive error on held out data. When combined with a conditional randomization testing procedure, the model discovers markers of therapeutic response that recapitulate known biology and suggest new avenues for investigation. All code for the article is publicly available at https://github.com/tansey/deep-dose-response.

Sparse HP filter: Finding kinks in the COVID-19 contact rate

In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases. We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks. We term it the sparse HP filter and apply it to daily data from five countries: Canada, China, South Korea, the UK and the US. Our new method yields the kinks that are well aligned with actual events in each country. We find that the sparse HP filter provides a fewer kinks than theℓ 1 trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP andℓ 1 trend filters. Ultimately, we propose to use time-varying contact growth rates to document and monitor outbreaks of COVID-19.

Compressed sensing of large-scale local field potentials using adaptive sparsity analysis and Non-convex Optimization

OBJECTIVE

Energy consumption is a critical issue in resource-constrained wireless neural recording applications with limited data bandwidth. Compressed sensing (CS) has emerged as a powerful framework in addressing this issue owing to its highly efficient data compression procedure. In this paper, a CS-based approach termed Simultaneous Analysis Non-Convex Optimization (SANCO) is proposed for large-scale, multi-channel local field potentials (LFPs) recording.

APPROACH

The SANCO method consists of three parts: (1) the analysis model is adopted to reinforce sparsity of the multi-channel LFPs, therefore overcoming the drawbacks of conventional synthesis models. (2) An optimal continuous order difference matrix is constructed as the analysis operator, enhancing the recovery performance while saving both computational resources and data storage space. (3) A non-convex optimizer that can by efficiently solved with alternating direction method of multipliers (ADMM) is developed for multi-channel LFPs reconstruction.

MAIN RESULTS

Experimental results on real datasets reveal that the proposed approach outperforms state-of-the-art CS methods in terms of both recovery quality and computational efficiency.

SIGNIFICANCE

Energy efficiency of the SANCO make it an ideal candidate for resource-constrained, large scale wireless neural recording. Particularly, the proposed method ensures that the key features of LFPs had little degradation even when data are compressed by 16x, making it very suitable for long term wireless neural recording applications.

Simultaneous spatial smoothing and outlier detection using penalized regression, with application to childhood obesity surveillance from electronic health records

Electronic health records (EHRs) have become a platform for data-driven granular-level surveillance in recent years. In this paper, we make use of EHRs for early prevention of childhood obesity. The proposed method simultaneously provides smooth disease mapping and outlier information for obesity prevalence that are useful for raising public awareness and facilitating targeted intervention. More precisely, we consider a penalized multilevel generalized linear model. We decompose regional contribution into smooth and sparse signals, which are automatically identified by a combination of fusion and sparse penalties imposed on the likelihood function. In addition, we weigh the proposed likelihood to account for the missingness and potential nonrepresentativeness arising from the EHR data. We develop a novel alternating minimization algorithm, which is computationally efficient, easy to implement, and guarantees convergence. Simulation studies demonstrate superior performance of the proposed method. Finally, we apply our method to the University of Wisconsin Population Health Information Exchange database.

Identification, Decomposition and Segmentation of Impulsive Vibration Signals with Deterministic Components-A Sieving Screen Case Study

Condition monitoring is a well-established field of research; however, for industrial applications, one may find some challenges. They are mostly related to complex design, a specific process performed by the machine, time-varying load/speed conditions, and the presence of non-Gaussian noise. A procedure for vibration analysis from the sieving screen used in the raw material industry is proposed in the paper. It is more for pre-processing than the damage detection procedure. The idea presented here is related to identification and extraction of two main types of components: (i) deterministic (D)—related to the unbalanced shaft(s) and (ii) high amplitude, impulsive component randomly (R) appeared in the vibration due to pieces of ore falling down of moving along the deck. If we could identify these components, then we will be able to perform classical diagnostic procedures for local damage detection in rolling element bearing. As deterministic component may be AM/FM modulated and each impulse may appear with different amplitude and damping, there is a need for an automatic procedure. We propose a method for signal processing that covers two main steps: (a) related to R/D decomposition and including signal segmentation to neglect AM/FM modulations, iterative sine wave fitting using the least square method (for each segment), signal filtering technique by subtraction fitted sine from the raw signal, the definition of the criterion to stop iteration by residuals analysis, (b) impulse segmentation and description (beginning, end, max amplitude) that contains: detection of the number of impulses in a decomposed random part of the raw signal, detection of the max value of each impulse, statistical analysis (probability density function) of max value to find regime-switching), modeling of the envelope of each impulse for samples that protrude from the signal, extrapolation (forecasting) envelope shape for samples hidden in the signal. The procedure is explained using simulated and real data. Each step is very easy to implement and interpret thus the method may be used in practice in a commercial system.

Joint penalized spline modeling of multivariate longitudinal data, with application to HIV-1 RNA load levels and CD4 cell counts

Motivated by the need to jointly model the longitudinal trajectories of HIV viral load levels and CD4 counts during the primary infection stage, we propose a joint penalized spline modeling approach that can be used to model the repeated measurements from multiple biomarkers of various types (eg, continuous, binary) simultaneously. This approach allows for flexible trajectories for each marker, accounts for potentially time-varying correlation between markers, and is robust to misspecification of knots. Despite its advantages, the application of multivariate penalized spline models, especially when biomarkers may be of different data types, has been limited in part due to its seemingly complexity in implementation. To overcome this, we describe a procedure that transforms the multivariate setting to the univariate one, and then makes use of the generalized linear mixed effect model representation of a penalized spline model to facilitate its implementation with standard statistical software. We performed simulation studies to evaluate the validity and efficiency through joint modeling of correlated biomarkers measured longitudinally compared to the univariate modeling approach. We applied this modeling approach to longitudinal HIV-1 RNA load and CD4 count data from Southern African cohorts to estimate features of the joint distributions such as the correlation and the proportion of subjects with high viral load levels and high CD4 cell counts over time.

Adaptive nonparametric regression with the K-nearest neighbour fused lasso

The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the [Formula: see text]-nearest-neighbours fused lasso, involves computing the [Formula: see text]-nearest-neighbours graph of the design points and then performing the fused lasso over this graph. We show that this procedure has a number of theoretical advantages over competing methods: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the [Formula: see text]-nearest-neighbours approach. In a simulation study and an application to flu data, we show that excellent results are obtained. For completeness, we also study an estimator that makes use of an [Formula: see text]-graph rather than a [Formula: see text]-nearest-neighbours graph and contrast it with the [Formula: see text]-nearest-neighbours fused lasso.

Characterizing and inferring quantitative cell cycle phase in single-cell RNA-seq data analysis

Cellular heterogeneity in gene expression is driven by cellular processes, such as cell cycle and cell-type identity, and cellular environment such as spatial location. The cell cycle, in particular, is thought to be a key driver of cell-to-cell heterogeneity in gene expression, even in otherwise homogeneous cell populations. Recent advances in single-cell RNA-sequencing (scRNA-seq) facilitate detailed characterization of gene expression heterogeneity and can thus shed new light on the processes driving heterogeneity. Here, we combined fluorescence imaging with scRNA-seq to measure cell cycle phase and gene expression levels in human induced pluripotent stem cells (iPSCs). By using these data, we developed a novel approach to characterize cell cycle progression. Although standard methods assign cells to discrete cell cycle stages, our method goes beyond this and quantifies cell cycle progression on a continuum. We found that, on average, scRNA-seq data from only five genes predicted a cell's position on the cell cycle continuum to within 14% of the entire cycle and that using more genes did not improve this accuracy. Our data and predictor of cell cycle phase can directly help future studies to account for cell cycle-related heterogeneity in iPSCs. Our results and methods also provide a foundation for future work to characterize the effects of the cell cycle on expression heterogeneity in other cell types.

Deconvolution of Sustained Neural Activity From Large-Scale Calcium Imaging Data

Recent technological advances in light-sheet microscopy make it possible to perform whole-brain functional imaging at the cellular level with the use of Ca²⁺ indicators. The outstanding spatial extent and resolution of this type of data open unique opportunities for understanding the complex organization of neuronal circuits across the brain. However, the analysis of this data remains challenging because the observed variations in fluorescence are, in fact, noisy indirect measures of the neuronal activity. Moreover, measuring over large field-of-view negatively impact temporal resolution and signal-to-noise ratio, which further impedes conventional spike inference. Here we argue that meaningful information can be extracted from large-scale functional imaging data by deconvolving with the calcium response and by modeling moments of sustained neuronal activity instead of individual spikes. Specifically, we characterize the calcium response by a linear system of which the inverse is a differential operator. This operator is then included in a regularization term promoting sparsity of activity transients through generalized total variation. Our results illustrate the numerical performance of the algorithm on simulated signals; i.e., we show the firing rate phase transition at which our model outperforms spike inference. Finally, we apply the proposed algorithm to experimental data from zebrafish larvæ. In particular, we show that, when applied to a specific group of neurons, the algorithm retrieves neural activation that matches the locomotor behavior unknown to the method.