Latent States Research Articles

A Neural Phillips Curve and a Deep Output Gap

Many problems plague empirical Phillips curves (PCs). Among them is the hurdle that the two key components, inflation expectations and the output gap, are both unobserved. Traditional remedies include proxying for the absentees or extracting them via assumptions-heavy filtering procedures. I propose an alternative route: a Hemisphere Neural Network (HNN) whose architecture yields a final layer where components can be interpreted as latent states within a Neural PC. First, HNN conducts the supervised estimation of nonlinearities that arise when translating a high-dimensional set of observed regressors into latent states. Second, forecasts are economically interpretable. Among other findings, the contribution of real activity to inflation appears understated in traditional PCs. In contrast, HNN captures the 2021 upswing in inflation and attributes it to a large positive output gap starting from late 2020. The unique path of HNN’s gap comes from dispensing with unemployment and GDP in favor of an amalgam of nonlinearly processed alternative tightness indicators.

Compositional pretraining improves computational efficiency and matches animal behavior on complex tasks.

1Recurrent neural networks (RNN) are ubiquitously used in neuroscience to capture both neural dynamics and behaviors of living systems. However, when it comes to complex cognitive tasks, training RNNs with traditional methods can prove difficult and fall short of capturing crucial aspects of animal behavior. Here we propose a principled approach for identifying and incorporating compositional tasks as part of RNN training. Taking as target a temporal wagering task previously studied in rats, we design a pretraining curriculum of simpler cognitive tasks that reflect relevant sub-computations. We show that this pretraining substantially improves learning efficacy and is critical for RNNs to adopt similar strategies as rats, including long-timescale inference of latent states, which conventional pretraining approaches fail to capture. Mechanistically, our pretraining supports the development of slow dynamical systems features needed for implementing both inference and value-based decision making. Overall, our approach is an important step for endowing RNNs with relevant inductive biases, which is important when modeling complex behaviors that rely on multiple cognitive computations.

Gamma Process Based Degradation Model with Fractional Gaussian Noise

In modern industrial and engineering systems, stochastic degradation models are widely used for reliability analysis and maintenance decision-making. However, due to imperfect sensors and environmental influences, it is difficult to directly observe the latent degradation states. Traditional degradation models typically assume that measurement errors have simple statistical properties, but this assumption often does not hold in practical applications. To address this issue, this paper constructs a degradation model based on the Gamma process (GP) and assumes that measurement noise can be characterized by the fractional Gaussian noise (FGN). Furthermore, this paper proposes a method combining Gibbs sampling with the stochastic expectation-maximization (SEM) algorithm to achieve efficient estimation of the model parameters and accurate inference of the latent degradation states. Simulation results indicate that the proposed model exhibits better generalizability compared to the GP model with Gaussian noise.

Learning probability distributions of sensory inputs with Monte Carlo predictive coding.

It has been suggested that the brain employs probabilistic generative models to optimally interpret sensory information. This hypothesis has been formalised in distinct frameworks, focusing on explaining separate phenomena. On one hand, classic predictive coding theory proposed how the probabilistic models can be learned by networks of neurons employing local synaptic plasticity. On the other hand, neural sampling theories have demonstrated how stochastic dynamics enable neural circuits to represent the posterior distributions of latent states of the environment. These frameworks were brought together by variational filtering that introduced neural sampling to predictive coding. Here, we consider a variant of variational filtering for static inputs, to which we refer as Monte Carlo predictive coding (MCPC). We demonstrate that the integration of predictive coding with neural sampling results in a neural network that learns precise generative models using local computation and plasticity. The neural dynamics of MCPC infer the posterior distributions of the latent states in the presence of sensory inputs, and can generate likely inputs in their absence. Furthermore, MCPC captures the experimental observations on the variability of neural activity during perceptual tasks. By combining predictive coding and neural sampling, MCPC can account for both sets of neural data that previously had been explained by these individual frameworks.

Stream of variation modeling and monitoring for heterogeneous profiles in multi-stage manufacturing processes

ABTRACT Advanced manufacturing systems typically involve multiple operating stages, where in-process data are observed in the form of profiles that contain rich information for process monitoring. Emerging methodologies have been developed for multi-stage profile monitoring. However, the cases where different stages’ profiles are heterogeneous and variations propagate over stages have not been addressed so far. To this end, this article proposes a heterogeneous profiles-based stream of variation (HP-SoV) framework for multi-stage manufacturing process monitoring. It uses functional decomposition to extract features of heterogeneous profiles from different stages, where the decomposition coefficients are regarded as latent states that propagate along consecutive stages to capture the variation propagation. HP-SoV includes many existing models as its special cases, and enjoys an efficient inference algorithm via maximum likelihood estimation. Based on the one-step-ahead forecast errors of HP-SoV, a group monitoring scheme is further developed for online monitoring. Extensive numerical studies explore the modeling robustness and monitoring effectiveness of HP-SoV under different settings. A case study demonstrates the applicability of HP-SoV in multi-stage process monitoring for heterogeneous profiles.

Touchscreen response precision is sensitive to the explore/exploit tradeoff.

The explore/exploit tradeoff is a fundamental property of choice selection during reward-guided decision making. In perceptual decision making, higher certainty decisions are more motorically precise, even when the decision does not require motor accuracy. However, while we can parametrically control uncertainty in perceptual tasks, we do not know what variables - if any - shape motor precision and reflect subjective certainty during reward-guided decision making. Touchscreens are increasingly used across species to measure choice, but provide no tactile feedback on whether an action is precise or not, and therefore provide a valuable opportunity to determine whether actions differ in precision due to explore/exploit state, reward, or individual variables. We find all three of these factors exert independent drives towards increased precision. During exploit states, successive touches to the same choice are closer together than those made in an explore state, consistent with exploit states reflecting higher certainty and/or motor stereotypy in responding. However, exploit decisions might be expected to be rewarded more frequently than explore decisions. We find that exploit choice precision is increased independently of a separate increase in precision due to immediate past reward, suggesting multiple mechanisms regulating choice precision. Finally, we see evidence that male mice in general are less precise in their interactions with the touchscreen than females, even when exploiting a choice. These results suggest that as exploit behavior emerges in reward-guided decision making, individuals become more motorically precise reflecting increased certainty, even when decision choice does not require additional motor accuracy, but this is influenced by individual differences and prior reward. These data uncover the hidden potential for touchscreen tasks in any species to uncover the latent neural states that unite cognition and movement.

The Chains of the Clusters of Latent States in DNA Sequencing

The Chains of the Clusters of Latent States in DNA Sequencing

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

ABSTRACT Pulsar timing arrays (PTA) can detect continuous nanohertz gravitational waves (GW) emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a GW from a single source. The modulation is the sum of terms proportional to the GW strain at the Earth and at every pulsar in the array. Here, we generalize previous state-space formulations of the PTA problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by 14 per cent. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

Impaired brain ability of older adults to transit and persist to latent states with well-organized structures at wakeful rest.

The intrinsic brain functional network organization continuously changes with aging. By integrating spatial and temporal information, the process of how brain networks temporally reconfigure and remain well-organized spatial structure largely reflects the brain function, thereby holds the potential to capture its age-related declines. In this study, we examined the spatiotemporal brain dynamics from resting-state functional Magnetic Resonance Imaging (fMRI) data of healthy young and older adults using a Hidden Markov Model (HMM). Six brain states were generated by HMM, with the young group showing higher fractional occupancy and mean dwell time in states 1, 3, and 4 (SY1, SY2 and SY3), and the older group in states 2, 5, and 6 (SO1, SO2 and SO3). Importantly, comparisons of transition probabilities revealed that the older group showed a reduced brain ability to transition into states dominated by the younger group, as well as a diminished capacity to persist in them. Moreover, graph analysis revealed that these young-specific states exhibited higher modularity and k-coreness. Collectively, these findings suggested that the older group showed impaired brain ability of both transition into and sustain well spatially organized states. This emphasized that the temporal changes in brain state organization, rather than its static mode, could be a key biomarker for detecting age-related functional decline. These insights may pave the way for targeted interventions aimed at mitigating cognitive decline in the aging population.

Supervised structure learning

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move—in the ensuing schemes—is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information, where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states—and their characteristic paths or dynamics.

Semi-Markov process-driven maintenance scheduling for Tainter gate system considering multiplelimit states

In extended periods of operation, Taiwan’s reservoir electromechanical systems increasingly require substantial maintenance. This research adopts the semi-Markov process, which accommodates non-exponential distribution of state durations, to formulate optimal maintenance strategies for Tainter gate systems that are noted for their prolonged dormancy and significant operational uncertainties. The methodology initiates with the estimation of failure probabilities across four condition states, analyzing deterioration through the Weibull distribution for both general and latent limit states. The general limit state accounts for time-induced deterioration and effects of dormancy using a Bayesian–Weibull first-order reliability method, while the latent limit state addresses activation failures. Employing the semi-Markov process, an annual transition matrix is computed and combined with failure probabilities to assess the Tainter gates’ system reliability. To identify the most efficient maintenance schedule, a genetic algorithm is applied, targeting the minimization of failure probabilities for both limit states below predefined thresholds and cost reduction. Numerical simulations validate the framework’s efficacy, demonstrating its potential to enhance maintenance planning objectivity and decrease dependence on subjective assessments. The findings highlight the predominance of the general limit state in dictating system failure and underscore the risk Tainter gates face during transition from dormancy to activation, emphasizing the need for thorough monitoring.

A latent variable approach to jointly modeling longitudinal and cumulative event data using a weighted two-stage method.

Ecological momentary assessment (EMA), a data collection method commonly employed in mHealth studies, allows for repeated real-time sampling of individuals' psychological, behavioral, and contextual states. Due to the frequent measurements, data collected using EMA are useful for understanding both the temporal dynamics in individuals' states and how these states relate to adverse health events. Motivated by data from a smoking cessation study, we propose a joint model for analyzing longitudinal EMA data to determine whether certain latent psychological states are associated with repeated cigarette use. Our method consists of a longitudinal submodel-a dynamic factor model-that models changes in the time-varying latent states and a cumulative risk submodel-a Poisson regression model-that connects the latent states with the total number of events. In the motivating data, both the predictors-the underlying psychological states-and the event outcome-the number of cigarettes smoked-are partially unobservable; we account for this incomplete information in our proposed model and estimation method. We take a two-stage approach to estimation that leverages existing software and uses importance sampling-based weights to reduce potential bias. We demonstrate that these weights are effective at reducing bias in the cumulative risk submodel parameters via simulation. We apply our method to a subset of data from a smoking cessation study to assess the association between psychological state and cigarette smoking. The analysis shows that above-average intensities of negative mood are associated with increased cigarette use.

GAP-LSTM: Graph-Based Autocorrelation Preserving Networks for Geo-Distributed Forecasting.

Forecasting methods are important decision support tools in geo-distributed sensor networks. However, challenges such as the multivariate nature of data, the existence of multiple nodes, and the presence of spatio-temporal autocorrelation increase the complexity of the task. Existing forecasting methods are unable to address these challenges in a combined manner, resulting in a suboptimal model accuracy. In this article, we propose GAP-LSTM, a novel geo-distributed forecasting method that leverages the synergic interaction of graph convolution, attention-based long short-term memory (LSTM), 2-D-convolution, and latent memory states to effectively exploit spatio-temporal autocorrelation in multivariate data generated by multiple nodes, resulting in improved modeling capabilities. Our extensive evaluation, involving real-world datasets on traffic, energy, and pollution domains, showcases the ability of our method to outperform state-of-the-art forecasting methods. An ablation study confirms that all method components provide a positive contribution to the accuracy of the extracted forecasts. The method also provides an interpretable visualization that complements forecasts with additional insights for domain experts.

Modelling network motifs as higher order interactions: a statistical inference based approach

The prevalent approach to motif analysis seeks to describe the local connectivity structure of networks by identifying subgraph patterns that appear significantly more often in a network then expected under a null model that conserves certain features of the original network. In this article we advocate for an alternative approach based on statistical inference of generative models where nodes are connected not only by edges but also copies of higher order subgraphs. These models naturally lead to the consideration of latent states that correspond to decompositions of networks into higher order interactions in the form of subgraphs that can have the topology of any simply connected motif. Being based on principles of parsimony the method can infer concise sets of motifs from within thousands of candidates allowing for consistent detection of larger motifs. The inferential approach yields not only a set of statistically significant higher order motifs but also an explicit decomposition of the network into these motifs, which opens new possibilities for the systematic study of the topological and dynamical implications of higher order connectivity structures in networks. After briefly reviewing core concepts and methods, we provide example applications to empirical data sets and discuss how the inferential approach addresses current problems in motif analysis and explore how concepts and methods common to motif analysis translate to the inferential framework.

Personalizing driver safety interfaces via driver cognitive factors inference

Recent advances in AI and intelligent vehicle technology hold the promise of revolutionizing mobility and transportation through advanced driver assistance systems (ADAS). Certain cognitive factors, such as impulsivity and inhibitory control have been shown to relate to risky driving behavior and on-road risk-taking. However, existing systems fail to leverage such factors in assistive driving technologies adequately. Varying the levels of these cognitive factors could influence the effectiveness and acceptance of ADAS interfaces. We demonstrate an approach for personalizing driver interaction via driver safety interfaces that are are triggered based on the inference of the driver’s latent cognitive states from their driving behavior. To accomplish this, we adopt a data-driven approach and train a recurrent neural network to infer impulsivity and inhibitory control from recent driving behavior. The network is trained on a population of human drivers to infer impulsivity and inhibitory control from recent driving behavior. Using data collected from a high-fidelity vehicle motion simulator experiment, we demonstrate the ability to deduce these factors from driver behavior. We then use these inferred factors to determine instantly whether or not to engage a driver safety interface. This approach was evaluated using leave-one-out cross validation using actual human data. Our evaluations reveal that our personalized driver safety interface that captures the cognitive profile of the driver is more effective in influencing driver behavior in yellow light zones by reducing their inclination to run through them.

Improved allele-specific single-cell copy number estimation in low-coverage DNA-sequencing.

Advances in whole-genome single-cell DNA sequencing (scDNA-seq) have led to the development of numerous methods for detecting copy number aberrations (CNAs), a key driver of genetic heterogeneity in cancer. While most of these methods are limited to the inference of total copy number, some recent approaches now infer allele-specific CNAs using innovative techniques for estimating allele-frequencies in low coverage scDNA-seq data. However, these existing allele-specific methods are limited in their segmentation strategies, a crucial step in the CNA detection pipeline. We present SEACON (Single-cell Estimation of Allele-specific COpy Numbers), an allele-specific copy number profiler for scDNA-seq data. SEACON uses a Gaussian Mixture Model to identify latent copy number states and breakpoints between contiguous segments across cells, filters the segments for high-quality breakpoints using an ensemble technique, and adopts several strategies for tolerating noisy read-depth and allele frequency measurements. Using a wide array of both real and simulated datasets, we show that SEACON derives accurate copy numbers and surpasses existing approaches under numerous experimental conditions, and identify its strengths and weaknesses. SEACON is implemented in Python and is freely available open-source from https://github.com/NabaviLab/SEACON and https://doi.org/10.5281/zenodo.12727008.

Modeling behavioral patterns of family violence aggressors

Background settingThe presumption that family violence will repeat and escalate is embedded in practices including risk assessment and case management. However, there is limited evidence that further episodes are inevitable, or that subsequent episodes will increase in severity. Therefore, we need to better understand temporal patterns in aggressor behavior to inform how risk is conceptualized in practice.MethodsFor a sample of 2115 family violence aggressors who came to police attention in Integrated Safety Response catchment areas in Aotearoa New Zealand, we collected information New Zealand Police routinely recorded about reported harm between 2018 and 2020. We used a hidden Markov model to estimate the latent (i.e., unmeasurable) states behind the information reported to police, and modeled aggressors’ movement between those states over time.ResultsWe identified three latent states. The first contained low or no reported harm, the second contained low probabilities of reported harm, and the third involved a high probability of reported verbal abuse and a moderate probability of reported physical violence. We identified four pathways through the latent states over the two-year follow-up period, which we called No reported harm, High reported harm, Low reported harm, and De-escalation.ConclusionsThe findings add to the body of research indicating that family violence aggressors do not inevitably repeat or escalate their harmful behavior, and that a small subset of cases account for a large proportion of reported harm. This study demonstrates how information that police routinely collect can be used to estimate aggressors’ latent behavioral states and model pathways communicating the probability that they will continue to come to police attention for family violence, contributing to improved risk assessment and practice.

Φ-DVAE: Physics-informed dynamical variational autoencoders for unstructured data assimilation

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be known. This prevents these methods from achieving a consistent model-data synthesis in configurations where the mapping from data-space to model-space is unknown. To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder (Φ-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations. Our approach combines a standard, possibly nonlinear, filter for the latent state-space model and a VAE, to assimilate the unstructured data into the latent dynamical system. Unstructured data, in our example systems, comes in the form of video data and velocity field measurements, however the methodology is suitably generic to allow for arbitrary unknown observation operators. A variational Bayesian framework is used for the joint estimation of the encoding, latent states, and unknown system parameters. To demonstrate the method, we provide case studies with the Lorenz-63 ordinary differential equation, and the advection and Korteweg-de Vries partial differential equations. Our results, with synthetic data, show that Φ-DVAE provides a data efficient dynamics encoding methodology which is competitive with standard approaches. Unknown parameters are recovered with uncertainty quantification, and unseen data are accurately predicted.

A sensory-motor theory of the neocortex.

Recent neurophysiological and neuroanatomical studies suggest a close interaction between sensory and motor processes across the neocortex. Here, I propose that the neocortex implements active predictive coding (APC): each cortical area estimates both latent sensory states and actions (including potentially abstract actions internal to the cortex), and the cortex as a whole predicts the consequences of actions at multiple hierarchical levels. Feedback from higher areas modulates the dynamics of state and action networks in lower areas. I show how the same APC architecture can explain (1) how we recognize an object and its parts using eye movements, (2) why perception seems stable despite eye movements, (3) how we learn compositional representations, for example, part-whole hierarchies, (4) how complex actions can be planned using simpler actions, and (5) how we form episodic memories of sensory-motor experiences and learn abstract concepts such as a family tree. I postulate a mapping of the APC model to the laminar architecture of the cortex and suggest possible roles for cortico-cortical and cortico-subcortical pathways.

The neuron as a direct data-driven controller

In the quest to model neuronal function amid gaps in physiological data, a promising strategy is to develop a normative theory that interprets neuronal physiology as optimizing a computational objective. This study extends current normative models, which primarily optimize prediction, by conceptualizing neurons as optimal feedback controllers. We posit that neurons, especially those beyond early sensory areas, steer their environment toward a specific desired state through their output. This environment comprises both synaptically interlinked neurons and external motor sensory feedback loops, enabling neurons to evaluate the effectiveness of their control via synaptic feedback. To model neurons as biologically feasible controllers which implicitly identify loop dynamics, infer latent states, and optimize control we utilize the contemporary direct data-driven control (DD-DC) framework. Our DD-DC neuron model explains various neurophysiological phenomena: the shift from potentiation to depression in spike-timing-dependent plasticity with its asymmetry, the duration and adaptive nature of feedforward and feedback neuronal filters, the imprecision in spike generation under constant stimulation, and the characteristic operational variability and noise in the brain. Our model presents a significant departure from the traditional, feedforward, instant-response McCulloch-Pitts-Rosenblatt neuron, offering a modern, biologically informed fundamental unit for constructing neural networks.