Sampling Zeros Research Articles

CARE: Large Precision Matrix Estimation for Compositional Data

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Secure Nonlinear Sampled-Data Control System Against Stealthy Attack: Multirate Approach

In this paper, we provide a novel defence strategy for a nonlinear sampled-data control system under zero-dynamics attacks. In a sampled data structure, sampling zeros induced by discretization make a system vulnerable to deception attacks. we analyze the dissipativity in the zero-dynamics part of the system equipped with a multi-rate setup and find conditions on sampling rates to neutralize the attacker's target plan. We show that, under some mild conditions, using multi-rate sampling in the nonlinear sampled-data system not only preserves the dissipativity property of the intrinsic zero-dynamics but also stabilizes the extrinsic zero-dynamics induced by the sample and hold process, and as a result attenuate the effects of attacks on the system stability. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

Overview of selected reinforcement learning solutions to several game theory problems

This paper collects several applications of reinforcement learning in solving some problems related to game theory. The methods were selected to possibly show variety of problems and approaches. Selections includes Thompson Sampling, Q-learning, DQN and AlphaGo Zero using Monte Carlo Tree Search algorithm. Paper attempts to show intuition behind proposed algorithms with shallow explaining of technical details. This approach aims at presenting overview of the topic without assuming deep knowledge about statistics and artificial intelligence.

The limiting zero dynamics of discrete-time system based on forward triangle sample-and-hold.

Zero dynamics have crucial effect on system analysis and controller design. In the control analysis process, system performance is influenced by the unstable zero dynamics, greatly. This study concerns with the properties of limiting zero dynamics when the signal of controlled continuous-time systems was reconstructed by forward triangle sample-and-hold (FTSH). FTSH is a newly sample and hold method in the signal reconstruction area. However, more theoretical details about the limiting zero dynamics of the resulting discrete-time systems need to be revealed. Firstly, the framework for the limiting zero dynamics in the situation of sufficiently small or large sample period is introduced. Furthermore, this study provides the stable conditions of limiting zeros in the two different sampling situations. The results indicate that one can select a suitable variable parameter value of FTSH to replace the sampling zeros of discrete-time system locate inside the stable region. This paper also reveals the truth that FTSH has the outstanding advantage compared with the BTSH using theoretical analysis method. Finally, example simulations verify the effectiveness of the results in this study.

A deep generative model for feasible and diverse population synthesis

An agent-based model (ABM) simulates actions and interactions of the synthetic agents to understand the system-level behaviour. The synthetic population, the key input to ABM, mimics the distribution of the individual-level attributes in the actual population. Since individual-level attributes of the entire population are unavailable, small-scale samples are generally used for population synthesis. Synthesizing the population by directly sampling from the small-scale samples ignores the possible attribute combinations that are observed in the actual population but do not exist in the small-scale samples, called ‘sampling zeros’. A deep generative model (DGM) can potentially synthesize the sampling zeros but at the expense of falsely generating the infeasible attribute combinations that should be ‘zero’ in the generated data but exist, called ‘structural zeros’. This study proposes a novel method to ensure that the generation of structural zeros is minimal while recovering the ignored sampling zeros. Two loss functions for regularizing the DGMs are devised to customize the training and applied to a generative adversarial network (GAN) and a variational autoencoder (VAE). The adopted metrics for feasibility and diversity of the synthetic population indicate the capability of generating sampling and structural zeros – lower generation probability of structural zeros and lower generation probability of sampling zeros indicate the higher feasibility and the lower diversity, respectively. Results show that the proposed loss functions achieve considerable performance improvement in the feasibility and diversity of the synthesized population over traditional models. The proposed VAE additionally generated 23.5 % of the population ignored by the sample with 79.2 % precision (i.e., the generation ratio of structural zeros and the total samples is 20.8 %), while the proposed GAN generated 18.3 % of the ignored population with 89.0 % precision. The proposed improvement in DGM generates a more feasible and diverse synthetic population. Since synthesizing the population is the first stage of ABM, the proposed approach improves the overall accuracy of the ABM by circumventing the error propagation to later modelling stages.

Modeling Method for Sampling Zeros of Sampled-data System with Time Delay in Generalized Sample Hold

Unstable zeros are widely known to dramatically curb the performance of controllers and the direct applications of several control algorithms. Time delay is a crucial research topic due to the prevalence of communication and computational delays in the control process. In particular, time delay exacerbates the possibility of continuous-time systems with stable zeros transforming into discrete-time systems with unstable zeros. For continuous-time systems with a relative degree greater than or equal to two, at least one zero of the corresponding discrete-time system converges to either marginally stable or unstable locations as the sampling time approaches zero. This study investigates the sampling zeros of discrete-time systems in the case of a generalized sample hold function (GSHF) with time delay. Moreover, it presents a novel modeling method and stability conditions of the limiting zeros for the discrete-time system. The results demonstrate that the stable properties of zeros for the time delay systems can be preserved in the discretization process when GSHF is applied for signal reconstruction when zero-order hold fails to do so. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method in this study.

HiCImpute: A Bayesian hierarchical model for identifying structural zeros and enhancing single cell Hi-C data.

Single cell Hi-C techniques enable one to study cell to cell variability in chromatin interactions. However, single cell Hi-C (scHi-C) data suffer severely from sparsity, that is, the existence of excess zeros due to insufficient sequencing depth. Complicating the matter further is the fact that not all zeros are created equal: some are due to loci truly not interacting because of the underlying biological mechanism (structural zeros); others are indeed due to insufficient sequencing depth (sampling zeros or dropouts), especially for loci that interact infrequently. Differentiating between structural zeros and dropouts is important since correct inference would improve downstream analyses such as clustering and discovery of subtypes. Nevertheless, distinguishing between these two types of zeros has received little attention in the single cell Hi-C literature, where the issue of sparsity has been addressed mainly as a data quality improvement problem. To fill this gap, in this paper, we propose HiCImpute, a Bayesian hierarchical model that goes beyond data quality improvement by also identifying observed zeros that are in fact structural zeros. HiCImpute takes spatial dependencies of scHi-C 2D data structure into account while also borrowing information from similar single cells and bulk data, when such are available. Through an extensive set of analyses of synthetic and real data, we demonstrate the ability of HiCImpute for identifying structural zeros with high sensitivity, and for accurate imputation of dropout values. Downstream analyses using data improved from HiCImpute yielded much more accurate clustering of cell types compared to using observed data or data improved by several comparison methods. Most significantly, HiCImpute-improved data have led to the identification of subtypes within each of the excitatory neuronal cells of L4 and L5 in the prefrontal cortex.

Stability of Zeros for Sampled-Data Models with Triangle Sample and Hold Implemented by Zero-Order Hold

This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold. For any controlled models in the modern industrial system, using a digital control strategy has been shown to provide the means to achieve the assigned objectives. In this process, one must utilize the sample and hold device to obtain the sampled-data models. Previous studies have shown that the triangle sample and hold can improve the stability properties of zeros of a sampled-data control system compared with zero-order hold. However, it is difficult to use triangle sample and hold in practice. In this paper, an approximated method of using triangle sample and hold is proposed. More importantly, on the basis of that method, we explicitly derive the corresponding accurate sampled-data model of controlled models. In addition, we also provide the expression for sampling zeros and the theorem for the stability of a linear control system in the fast sampling process. The results of this paper show that the proposed method has the same advantages as the accurate one. Finally, theoretical findings are validated through numerical simulations with different considerations.

Assessing Bayesian Semi‐Parametric Log‐Linear Models: An Application to Disclosure Risk Estimation

SummaryWe propose a method for identifying models with good predictive performance in the family of Bayesian log‐linear mixed models with Dirichlet process random effects for count data. Their wide applicability makes the assessment of model performance crucial in many fields, including disclosure risk estimation, which is the focus of the present work.Rather than assessing models on the whole contingency table, we target the specific objective of the analysis and propose a two‐stage model selection procedure aimed at limiting a form of bias arising in the process of model selection. Our proposal combines two different criteria: at the first stage, a path in the model search space is identified through a strongly penalized log‐likelihood; at the second, a small number of semi‐parametric models is evaluated through a context‐dependent score‐based information criterion. Tested on a variety of contingency tables, our method proves to be able to identify models with good predictive performance in a few steps, even in the presence of large tables with many sampling and structural zeros. We carefully discuss the proposed method in the context of the literature on model assessment and contextualize the illustrative application in the recent debate on statistical disclosure limitation. Finally, we provide examples of further applications in different research areas.

A zero inflated log-normal model for inference of sparse microbial association networks.

The advent of high-throughput metagenomic sequencing has prompted the development of efficient taxonomic profiling methods allowing to measure the presence, abundance and phylogeny of organisms in a wide range of environmental samples. Multivariate sequence-derived abundance data further has the potential to enable inference of ecological associations between microbial populations, but several technical issues need to be accounted for, like the compositional nature of the data, its extreme sparsity and overdispersion, as well as the frequent need to operate in under-determined regimes. The ecological network reconstruction problem is frequently cast into the paradigm of Gaussian Graphical Models (GGMs) for which efficient structure inference algorithms are available, like the graphical lasso and neighborhood selection. Unfortunately, GGMs or variants thereof can not properly account for the extremely sparse patterns occurring in real-world metagenomic taxonomic profiles. In particular, structural zeros (as opposed to sampling zeros) corresponding to true absences of biological signals fail to be properly handled by most statistical methods. We present here a zero-inflated log-normal graphical model (available at https://github.com/vincentprost/Zi-LN) specifically aimed at handling such "biological" zeros, and demonstrate significant performance gains over state-of-the-art statistical methods for the inference of microbial association networks, with most notable gains obtained when analyzing taxonomic profiles displaying sparsity levels on par with real-world metagenomic datasets.

On the implication of structural zeros as independent variables in regression analysis: applications to alcohol research

In alcohol studies, drinking outcomes such as number of days of any alcohol drinking (DAD) over a period of time do not precisely capture the differences among subjects in a study population of interest. For example, the value of 0 on DAD could mean that the subject was continually abstinent from drinking such as lifetime abstainers or the subject was alcoholic, but happened not to use any alcohol during the period of interest. In statistics, zeros of the first kind are called structural zeros, to distinguish them from the sampling zeros of the second type. As the example indicates, the structural and sampling zeros represent two groups of subjects with quite different psychosocial outcomes. In the literature on alcohol use, although many recent studies have begun to explicitly account for the differences between the two types of zeros in modeling drinking variables as a response, none has acknowledged the implications of the different types of zeros when such modeling drinking variables are used as a predictor. This paper serves as the first attempt to tackle the latter issue and illustrate the importance of disentangling the structural and sampling zeros by using simulated as well as real study data.

A Zero-Inflated Latent Dirichlet Allocation Model for Microbiome Studies.

The human microbiome consists of a community of microbes in varying abundances and is shown to be associated with many diseases. An important first step in many microbiome studies is to identify possible distinct microbial communities in a given data set and to identify the important bacterial taxa that characterize these communities. The data from typical microbiome studies are high dimensional count data with excessive zeros due to both absence of species (structural zeros) and low sequencing depth or dropout. Although methods have been developed for identifying the microbial communities based on mixture models of counts, these methods do not account for excessive zeros observed in the data and do not differentiate structural from sampling zeros. In this paper, we introduce a zero-inflated Latent Dirichlet Allocation model (zinLDA) for sparse count data observed in microbiome studies. zinLDA builds on the flexible Latent Dirichlet Allocation model and allows for zero inflation in observed counts. We develop an efficient Markov chain Monte Carlo (MCMC) sampling procedure to fit the model. Results from our simulations show zinLDA provides better fits to the data and is able to separate structural zeros from sampling zeros. We apply zinLDA to the data set from the American Gut Project and identify microbial communities characterized by different bacterial genera.

Simplified Realization of Zero Phase Error Tracking

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output of a continuous time transfer function of relative order greater than or equal to two. In this paper, we will note that the sampling zeros of the zero-order hold equivalent of chain of integrators, 1/sn, are configured for natural realization of zero phase error tracking. This property is exploited to realize a simplified realization of zero phase error tracking control for chain of integrators. The property can also be utilized for general transfer functions when the sampling period for digital control is small. The effectiveness of the proposed approach for general transfer functions is demonstrated by simulations.

Prediction of rare feature combinations in population synthesis: Application of deep generative modelling

Population synthesis is concerned with the generation of agents for agent-based modelling in many fields, such as economics, transportation, ecology and epidemiology. When the number of attributes describing the agents and/or their level of detail becomes large, survey data cannot densely support the joint distribution of the attributes in the population due to the curse of dimensionality. It leads to a situation where many attribute combinations are missing from the sample data while such combinations exist in the real population. In this case, it becomes essential to consider methods that are able to impute such missing information effectively. In this paper, we propose to use deep generative latent models. These models are able to learn a compressed representation of the data space, which when projected back to the original space, leads to an effective way of imputing information in the observed data space. Specifically, we employ the Wasserstein Generative Adversarial Network (WGAN) and the Variational Autoencoder (VAE) for a large-scale population synthesis application. The models are applied to a Danish travel survey with a feature-space of more than 60 variables and trained and tested using cross-validation. A new metric that applies to the evaluation of generative models in an unsupervised setting is proposed. It is based on the ability to generate diverse yet valid synthetic attribute combinations by comparing if the models can recover missing combinations (sampling zeros) while keeping truly impossible combinations (structural zeros) models at a minimum. For a low-dimensional experiment, the VAE, the marginal sampler and the fully random sampler generate 5%, 21% and 26% more structural zeros per sampling zero when compared to the WGAN. For a high dimensional case, these figures increase to 44%, 2217% and 170440% respectively. This research directly supports the development of agent-based systems and in particular cases where detailed socio-economic or geographical representations are required.

Angle Measurement of Fuse Using Linear Frequency Modulation System Based on C6678 MultiCore DSPs

Real-time angle measurement of missiles is as important as range measurement for precision strike in modern wars and fuse using linear frequency modulation (LFM) system has been equipped widely due to its good range resolution. However, angle measurement of fuse using LFM system hasn’t been realized. In order to achieve the accurate and rapid measurement of angle, this paper firstly derives the relationship between angle and phase of beat signal in the LFM system. Secondly, an arithmetic called AapFFT-CZT is proposed by sampling and inserting zeros based on all-phase Fourier Transform (apFFT) and Chirp Z Transform (CZT). Compared with traditional Fast Fourier Transform (FFT), AapFFT-CZT has higher accuracy and better anti-noise performance when used to measure angle. Thirdly, angle measurement utilizing AapFFT-CZT is performed successfully on single core of TMS320C6678. When there is no noise, accuracy of angle measurement is within 0.01°. When there is Gaussian white noise, accuracy is still within 0.25°. Last but not least, fast and parallel measurement on multiple cores is achieved. The results show that clocks consumed when using multiple cores is just 57% of clocks consumed when using single core. Therefore, angle can be measured accurately and quickly based on C6678 multi-core DSPs.

Modelling the number of antenatal care visits in Bangladesh to determine the risk factors for reduced antenatal care attendance.

The existence of excess zeros in the distribution of antenatal care (ANC) visits in Bangladesh raises the research question of whether there are two separate generating processes in taking ANC and the frequency of ANC. Thus the main objective of this study is to identify a proper count regression model for the number of ANC visits by pregnant women in Bangladesh covering the issues of overdispersion, zero-inflation, and intra-cluster correlation with an additional objective of determining risk factors for ANC use and its frequency. The data have been extracted from the nationally representative 2014 Bangladesh Demographic and Health Survey, where 22% of the total 4493 women did not take any ANC during pregnancy. Since these zero ANC visits can be either structural or sampling zeros, two-part zero-inflated and hurdle regression models are investigated along with the standard one-part count regression models. Correlation among response values has been accounted for by incorporating cluster-specific random effects in the models. The hurdle negative binomial regression model with cluster-specific random intercepts in both the zero and the count part is found to be the best model according to various diagnostic tools including likelihood ratio and uniformity tests. The results show that women who have poor education, live in poor households, have less access to mass media, or belong to the Sylhet and Chittagong regions are less likely to use ANC and also have fewer ANC visits. Additionally, women who live in rural areas, depend on family members' decisions to take health care, and have unintended pregnancies had fewer ANC visits. The findings recommend taking both cluster-specific random effects and overdispersion and zero-inflation into account in modelling the ANC data of Bangladesh. Moreover, safe motherhood programmes still need to pay particular attention to disadvantaged and vulnerable subgroups of women.

Towards a Simple Sampled-Data Control Law for Stably Invertible Linear Systems

A new high gain control law is proposed for stably invertible linear systems. The continuous-time case is first studied to set ideas. The extension to the sampled-data case is made difficult by the presence of sampling zeros. For continuous-time systems having relative degree greater than or equal to two, these zeros converge, as the sampling rate approaches zero, to either marginally stable or unstable locations. A methodology which specifically addresses the sampling zero issue is developed. The methodology uses an approximate model which includes, when appropriate, the asymptotic sampling zeros. The core idea is supported by simulation studies. Also, a preliminary theoretical analysis is provided for degree two, showing that the design based on the approximate model stabilizes the true system for the continuous and sampled-data cases.

Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions

We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model and its accuracy (measured in terms of the local truncation error) depend on the smoothness of the input and on the applied integration strategy, namely, the truncated Taylor series expansion. Moreover, the sampling zero dynamics of the discrete-time model are asymptotically characterized as the sampling period goes to zero, and it is shown that these zero dynamics converge to the asymptotic sampling zeros of the linear case.

Neutralizing zero dynamics attack on sampled-data systems via generalized holds

Zero dynamics attacks can be lethal to cyber–physical systems because they can be harmful to physical plants and impossible to detect. Fortunately, if the given continuous-time physical system is minimum phase, the attack is not so effective even if it cannot be detected. However, the situation can become unfavorable if one uses digital control by sampling the sensor measurement and using a zero-order hold for actuation because of the ‘sampling zeros.’ When the continuous-time system has a relative degree greater than two and the sampling period is small, the sampled-data system must have unstable zeros (even if the continuous-time system is minimum phase), so that the cyber–physical system becomes vulnerable to ‘sampling zero dynamics attack.’ In this paper, we present an idea to neutralize the zero dynamics attack for single-input and single-output sampled-data systems by shifting the unstable discrete-time zeros into stable ones. This idea is realized by employing the so-called ‘generalized hold’ which replaces a standard zero-order hold. It is shown that, under mild assumptions, a generalized hold exists which places the discrete-time zeros at desired positions. Furthermore, we formulate the design problem as an optimization problem whose performance index is related to the inter-sample behavior of the physical plant, and propose an optimal gain which alleviates the performance degradation caused by generalized hold as much as possible.

Nonlinear Sampled-Data Systems with a Generalized Hold Polynomial-Function for Fast Sampling Rates

It is well-known that such non-conventional digital control schemes, such as generalized sampled-data hold functions, have clear advantages over the conventional single-rate digital control systems. However, they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples. This paper investigates the zero dynamics of sampled-data models, as the sampling period tends to zero, composed of a new generalized hold polynomial function, a nonlinear continuous-time plant and a sampler in cascade. For a new design of generalized hold circuit, the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems, and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adjustment. Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed. Also, an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design, where the ordinary multirate sampled systems have a poor intersample behavior. It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics. The results presented here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.