Dynamic noise estimation: A generalized method for modeling noise fluctuations in decision-making.

Computational cognitive modeling is an important tool for understanding the processes supporting human and animal decision-making. Choice data in decision-making tasks are inherently noisy, and separating noise from signal can improve the quality of computational modeling. Common approaches to model decision noise often assume constant levels of noise or exploration throughout learning (e.g., the ϵ-softmax policy). However, this assumption is not guaranteed to hold - for example, a subject might disengage and lapse into an inattentive phase for a series of trials in the middle of otherwise low-noise performance. Here, we introduce a new, computationally inexpensive method to dynamically infer the levels of noise in choice behavior, under a model assumption that agents can transition between two discrete latent states (e.g., fully engaged and random). Using simulations, we show that modeling noise levels dynamically instead of statically can substantially improve model fit and parameter estimation, especially in the presence of long periods of noisy behavior, such as prolonged attentional lapses. We further demonstrate the empirical benefits of dynamic noise estimation at the individual and group levels by validating it on four published datasets featuring diverse populations, tasks, and models. Based on the theoretical and empirical evaluation of the method reported in the current work, we expect that dynamic noise estimation will improve modeling in many decision-making paradigms over the static noise estimation method currently used in the modeling literature, while keeping additional model complexity and assumptions minimal.

Elucidating the links between N2O dynamics and changes in microbial communities following saltwater intrusions.

Saltwater intrusion in estuarine ecosystems alters microbial communities as well as biogeochemical cycling processes and has become a worldwide problem. However, the impact of salinity intrusion on the dynamics of nitrous oxide (N2O) and associated microbial community are understudied. Here, we conducted field microcosms in a tidal estuary during different months (December, April and August) using dialysis bags, and microbes inside the bags encountered a change in salinity in natural setting. We then compared N2O dynamics in the microcosms with that in natural water. Regardless of incubation environment, saltwater intrusion altered the dissolved N2O depending on the initial saturation rates of N2O. While the impact of saltwater intrusion on N2O dynamics was consistent across months, the dissolved N2O was higher in summer than in winter. The N-related microbial communities following saltwater intrusion were dominated by denitrifers, with fewer nitrifiers and bacterial taxa involved in dissimilatory nitrate reduction to ammonium. While denitrification was a significant driver of N2O dynamics in the studied estuary, nitrifier-involved denitrification contributed to the additional production of N2O, evidenced by the strong associations with amoA genes and the abundance of Nitrospira. Higher N2O concentrations in the field microcosms than in natural water limited N2O consumption in the former, given the lack of an association with nosZ gene abundance. The differences in the N2O dynamics observed between the microcosms and natural water could be that the latter comprised not only indigenous microbes but also those accompanied with saltwater intrusion, and that immigrants might be functionally rich individuals and able to perform N transformation in multiple pathways. Our work provides the first quantitative assessment of in situ N2O concentrations in an estuary subjected to a saltwater intrusion. The results highlight the importance of ecosystem size and microbial connectivity in the source-sink dynamics of N2O in changing environments.

Testing for the Markov property in time series via deep conditional generative learning.

The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I error asymptotically, and has the power approaching one. Our proposal makes novel contributions in several ways. We utilise and extend state-of-the-art deep generative learning to estimate the conditional density functions, and establish a sharp upper bound on the approximation error of the estimators. We derive a doubly robust test statistic, which employs a nonparametric estimation but achieves a parametric convergence rate. We further adopt sample splitting and cross-fitting to minimise the conditions required to ensure the consistency of the test. We demonstrate the efficacy of the test through both simulations and the three data applications.

Changes of dissolved organic matter following salinity invasion in different seasons in a nitrogen rich tidal reach.

Dissolved organic matter (DOM) is a heterogeneous mixture of dissolved material found ubiquitously in aquatic systems and dissolved organic nitrogen is one of its most important components. We hypothesised nitrogen species and salinity intrusions affect the DOM changes. Here, using the nitrogen rich Minjiang River as an easily accessible natural laboratory 3 field surveys with 9 sampling sites (S1-S9) were conducted in November 2018, April and August 2019. The excitation emission matrices (EEMs) of DOM were explored with parallel factor (PARAFAC) and cosine-histogram similarity analysis. Four indices including fluorescence index (FI), biological index (BIX), humification index (HIX) and the fluorescent DOM (FDOM) were calculated and the impact of physicochemical properties was assessed. The results suggested that the highest salinities of 6.15, 2.98 and 10.10, during each campaign corresponded to DTN concentrations of 119.29-240.71, 149.12-262.42 and 88.27-155.29 µmol·L-1, respectively. PARAFAC analysis revealed the presence of tyrosine-like proteins (C1), tryptophan-like proteins or a combination of the peak N and tryptophan-like fluorophore (C2) and the humic-like material (C3). The EEMs in the upstream reach (i.e. S1-S3) were complex with larger spectra ranges, higher intensities and similar similarity. Subsequently, the fluorescence intensity of three components decreased significantly with low similarity of EEMs (i.e. S4-S7). At the downstream, the fluorescence levels dispersed significantly and no obvious peaks were seen except in August. In addition, FI and HIX increased, while BIX and FDOM decreased from upstream to downstream. The salinity positively correlated with FI and HIX, and negatively related to BIX and FDOM. Besides, the elevated DTN had a significant effect on the DOM fluorescence indices. Altogether, salinity intrusion and elevated nitrogen are relevant for the distribution of the DOM, which is helpful for the water management tracing the DOM source according to the on-line monitoring of salinity and nitrogen in estuaries.

Exploring the ozone pollution over the western Sichuan Basin, Southwest China: The impact of diurnal change in mountain-plains solenoid.

The Sichuan Basin (SCB), to the east of the Tibetan Plateau (TP), experiences severe ozone (O3) pollution. Unfavorable atmospheric diffusion conditions are considered the main causes of heavy air pollution over the basin. However, the meteorological impact of thermally driven mountain-plains solenoid (MPS) between the TP and SCB on O3 pollution has not been reported. Here we show the MPS driving the diurnal O3 changes in the atmospheric boundary layer over the SCB based on surface and high-resolution vertical observations, ERA5 reanalysis data, and the WRF-Chem model. The MPS shifts between upslope and easterly flows along the eastern slope of the TP and SCB during the day and downslope westerly flows to the western SCB at night. The daytime MPS flows drive the westward transport of O3-rich air mass in the atmospheric boundary layer from the polluted SCB and accumulate high O3 levels from the western edge of the SCB to the eastern slope of TP, subsequently aggravating O3 pollution in this region. After sunset, the MPS drainage flows carry air containing elevated O3 eastward downslope along the eastern slope of the TP into the nocturnal residual layer, enhancing the O3 concentrations aloft over the western SCB. The high-level O3 in the residual layer is transported downstream by nocturnal prevailing winds and contributes significantly to the next-day surface O3 buildup in the downwind region through daytime vertical mixing (~30 µg m-3 h-1). The present study reveals a transport mechanism driven by the MPS with coupling diurnal changes in the atmospheric boundary layer, which redistributes O3 over the basin and exacerbates O3 pollution along the western edge of the basin. This study has important implications for understanding meteorological drivers on atmospheric environment underlying the complex terrain.

Sequential Pathway Inference for Multimodal Neuroimaging Analysis.

Motivated by a multimodal neuroimaging study for Alzheimer's disease, in this article, we study the inference problem, i.e., hypothesis testing, of sequential mediation analysis. The existing sequential mediation solutions mostly focus on sparse estimation, while hypothesis testing is an utterly different and more challenging problem. Meanwhile, the few mediation testing solutions often ignore the potential dependency among the mediators, or cannot be applied to the sequential problem directly. We propose a statistical inference procedure to test mediation pathways when there are sequentially ordered multiple data modalities and each modality involves multiple mediators. We allow the mediators to be conditionally dependent, and the number of mediators within each modality to diverge with the sample size. We produce the explicit significance quantification and establish the theoretical guarantees in terms of asymptotic size, power, and false discovery control. We demonstrate the efficacy of the method through both simulations and an application to a multimodal neuroimaging pathway analysis of Alzheimer's disease.

Testing Mediation Effects Using Logic of Boolean Matrices.

A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is that the total number of potential paths that go through any mediator is super-exponential in the number of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this article, we propose a novel hypothesis testing procedure to evaluate individual mediation effects, while taking into account potential interactions among the mediators. Our proposal thus fills a crucial gap, and greatly extends the scope of existing mediation tests. Our key idea is to construct the test statistic using the logic of Boolean matrices, which enables us to establish the proper limiting distribution under the null hypothesis. We further employ screening, data splitting, and decorrelated estimation to reduce the bias and increase the power of the test. We show that our test can control both the size and false discovery rate asymptotically, and the power of the test approaches one, while allowing the number of mediators to diverge to infinity with the sample size. We demonstrate the efficacy of the method through simulations and a neuroimaging study of Alzheimer's disease. A Python implementation of the proposed procedure is available at https://github.com/callmespring/LOGAN.

Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation.

In this paper, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the "oracle" method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the de-sparsified Lasso estimator (van de Geer et al., 2014) and the decorrelated score statistic (Ning and Liu, 2017). Simulation studies and real data applications are presented to back up our theoretical findings.

Influence of Riverbed Incision and Hydrological Evolution on Water Quality and Water Age Based on Numerical Simulation: A Case Study of the Minjiang Estuary.

In recent years, problems such as water quality deterioration, saltwater invasion, and low oxygen have appeared in estuaries all over the world. The Minjiang River in Fujian, as a typical tidal estuary area, is facing these thorny problems. In this paper, the effects of topography and hydrologic evolution on the water age and water quality of the lower reaches of the Minjiang River were simulated by building a hydrodynamic and water quality model. The results show that: (1) It was found that the riverbed incision of the lower reaches of the Minjiang River led to the overall decline of river water level, the increase of river volume, and the increase of downstream water age, which eventually led to the decrease of dissolved oxygen (DO) and the deterioration of water quality in the downstream from Shuikou to Baiyantan. However, the decline of topography led to the increase of tidal volume in the estuary, the enhancement of the dilution effect of oxygen-rich water bodies in the open sea, and the increase of DO in the lower reaches of Baiyantan. (2) Under no tidal action, the concentration of pollutants in the water of the North Channel increased, the DO decreased, and the DO decreased from Baiyantan to the offshore water. After the enhancement of tidal action, the dilution of oxygen-enriched water from the offshore water increased, and the DO increased. (3) The hydrological and water quality characteristics of the upper part of the lower reaches of the Minjiang River were mainly controlled by topography, runoff, and pollutant discharge, which were more affected by the tidal current transport operation and pollutant discharge near the open sea. In recent decades, the deterioration of water quality and the aggravation of saltwater intrusion in the Minjiang River were closely related to the serious topographic downcutting. The results provide a scientific basis for revealing the deterioration of estuary water quality and long-term management of the estuary.

A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

In contrast to the classical "one size fits all" approach, precision medicine proposes the customization of individualized treatment regimes to account for patients' heterogeneity in response to treatments. Most of existing works in the literature focused on estimating optimal individualized treatment regimes. However, there has been less attention devoted to hypothesis testing regarding the existence of overall qualitative treatment effects, especially when there is a large number of prognostic covariates. When covariates don't have qualitative treatment effects, the optimal treatment regime will assign the same treatment to all patients regardless of their covariate values. In this paper, we consider testing the overall qualitative treatment effects of patients' prognostic covariates in a high dimensional setting. We propose a sample splitting method to construct the test statistic, based on a nonparametric estimator of the contrast function. When the dimension of covariates is large, we construct the test based on sparse random projections of covariates into a low-dimensional space. We prove the consistency of our test statistic. In the regular cases, we show the asymptotic power function of our test statistic is asymptotically the same as the "oracle" test statistic which is constructed based on the "optimal" projection matrix. Simulation studies and real data applications validate our theoretical findings.

Salt intrusion alters nitrogen cycling in tidal reaches as determined in field and laboratory investigations.

Salinization is a growing problem throughout the world and poses a threat especially to freshwater ecosystems. However, much remains to be learned about the mechanisms by which salinity impacts microbially mediated biogeochemical processes. Elevated nitrogen (N) concentrations in estuarine ecosystems have led to their eutrophication, but the relationship between N transformation and the functional genes involved in the response to saltwater intrusion is poorly understood. Here, using the Minjiang River, a tidal river in southeastern China as an easily accessible natural laboratory, we conducted a 2-year field survey to investigate N speciation during ebb and flood tides. Then, in a laboratory experiment we simulated the varying degrees of salt intrusion that occur in natural tidal reaches. The microcosm study allowed quantitative assessments of N transformation and functional gene responses. The field surveys showed that concentrations of NH4+ rose during flood tides, while the concentrations of NO3- and total N fluctuated. In the microcosms, NO3- concentrations decreased in response to salt pulses, due to simultaneous declines in the abundance of genes responsible for nitrification and increases in the abundance of those involved in dissimilatory nitrate reduction to ammonium (DNRA). The elevated salinity led to increased yields of NH4+, a response that correlated positively with the abundance of nrfA genes, involved in DNRA. Furthermore, an increase in salinity promoted N2O accumulation during the denitrification process. Altogether, our study suggests that saltwater intrusion leads to a decrease in nitrification while favoring N transformation via denitrification and DNRA and that N2O accumulation in the water is dependent on the strength of the salt pulse.

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.

This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

ON TESTING CONDITIONAL QUALITATIVE TREATMENT EFFECTS.

Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed definition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and non-negligible power against some nonstandard local alternatives. The empirical performance of the proposed tests are evaluated by simulations and an application to an AIDS data set.

Determining the Number of Latent Factors in Statistical Multi-Relational Learning.

Statistical relational learning is primarily concerned with learning and inferring relationships between entities in large-scale knowledge graphs. Nickel et al. (2011) proposed a RESCAL tensor factorization model for statistical relational learning, which achieves better or at least comparable results on common benchmark data sets when compared to other state-of-the-art methods. Given a positive integer s, RESCAL computes an s-dimensional latent vector for each entity. The latent factors can be further used for solving relational learning tasks, such as collective classification, collective entity resolution and link-based clustering. The focus of this paper is to determine the number of latent factors in the RESCAL model. Due to the structure of the RESCAL model, its log-likelihood function is not concave. As a result, the corresponding maximum likelihood estimators (MLEs) may not be consistent. Nonetheless, we design a specific pseudometric, prove the consistency of the MLEs under this pseudometric and establish its rate of convergence. Based on these results, we propose a general class of information criteria and prove their model selection consistencies when the number of relations is either bounded or diverges at a proper rate of the number of entities. Simulations and real data examples show that our proposed information criteria have good finite sample properties.

Maximin Projection Learning for Optimal Treatment Decision with Heterogeneous Individualized Treatment Effects.

A saline feature of data from clinical trials and medical studies is inhomogeneity. Patients not only differ in baseline characteristics, but also the way they respond to treatment. Optimal individualized treatment regimes are developed to select effective treatments based on patient's heterogeneity. However, the optimal treatment regime might also vary for patients across different subgroups. In this paper, we mainly consider patient's heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups. We propose a new maximin-projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation. Based on estimated optimal treatment regimes for all subgroups, the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming (QCLP) problem, which can be efficiently computed by interior-point methods. Consistency and asymptotic normality of the estimator is established. Numerical examples show the reliability of the proposed methodology.

HIGH-DIMENSIONAL A-LEARNING FOR OPTIMAL DYNAMIC TREATMENT REGIMES.

Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such as patient's genetic information, demographic characteristics, medical history and clinical measurements over time are available, but not all of them are necessary for making treatment decision. This makes variable selection an emerging need in precision medicine. In this paper, we propose a penalized multi-stage A-learning for deriving the optimal dynamic treatment regime when the number of covariates is of the non-polynomial (NP) order of the sample size. To preserve the double robustness property of the A-learning method, we adopt the Dantzig selector which directly penalizes the A-leaning estimating equations. Oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established. Empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the STAR*D study.

A Massive Data Framework for M-Estimators with Cubic-Rate.

The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing the asymptotic distribution of the aggregated M-estimators using a weighted average with weights depending on the subgroup sample sizes. Under certain condition on the growing rate of the number of subgroups, the resulting aggregated estimators are shown to have faster convergence rate and asymptotic normal distribution, which are more tractable in both computation and inference than the original M-estimators based on pooled data. Our theory applies to a wide class of M-estimators with cube root convergence rate, including the location estimator, maximum score estimator and value search estimator. Empirical performance via simulations and a real data application also validate our theoretical findings.

Analysis and numerical simulation of natural and human-caused low dissolved oxygen in the Minjiang River Estuary.

The Minjiang River, a typical tidal channel in Southeast China, plays an important role in the supply of drinking water, flood control and drought relief, farming and navigation, as well as shipping and other functions. Dissolved oxygen (DO), as a basic living condition for aquatic biota, has been deteriorating in the Minjiang River in recent years. In order to understand how the spatial distribution of DO responds to river discharge, nutrient loading and water temperature, a three-dimensional Environmental Fluid Dynamics Code model was used to simulate water age and the distribution of DO in the Minjiang River. The model presented in this paper was used for water resource and water quality simulations under various physical, chemical, and biological scenarios. Sensitivity simulation results indicated that the three factors had a significant impact on the spatial distribution variation of DO in the Minjiang River. Increased river discharge or split ratio of the North Channel resulted in decreased water age and increased DO. Increased nutrient loading and water temperature caused lower DO. In order to protect coastal environments in the Minjiang River, river discharge should be increased and pollutants of local cities should be reduced during the high temperature and drought period.

Robust learning for optimal treatment decision with NP-dimensionality.

In order to identify important variables that are involved in making optimal treatment decision, Lu, Zhang and Zeng (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the misspecification of the conditional mean model. Two problems arise: (i) in a world of explosively big data, effective methods are needed to handle ultra-high dimensional data set, for example, with the dimension of predictors is of the non-polynomial (NP) order of the sample size; (ii) both the propensity score and conditional mean models need to be estimated from data under NP dimensionality. In this paper, we propose a robust procedure for estimating the optimal treatment regime under NP dimensionality. In both steps, penalized regressions are employed with the non-concave penalty function, where the conditional mean model of the response given predictors may be misspecified. The asymptotic properties, such as weak oracle properties, selection consistency and oracle distributions, of the proposed estimators are investigated. In addition, we study the limiting distribution of the estimated value function for the obtained optimal treatment regime. The empirical performance of the proposed estimation method is evaluated by simulations and an application to a depression dataset from the STAR*D study.

Factors Contributing to Hypoxia in the Minjiang River Estuary, Southeast China.

Dissolved oxygen (DO) is not only a fundamental parameter of coastal water quality, but also an indication of organics decomposed in water and their degree of eutrophication. There has been a concern about the deterioration of dissolved oxygen conditions in the Minjiang River Estuary, the longest river in Fujian Province, Southeast China. In this study, the syntheses effects on DO was analyzed by using a four year time series of DO concentration and ancillary parameters (river discharge, water level, and temperature) from the Fuzhou Research Academy of Environmental Sciences, at three automated stations along the Minjiang River Estuary. Hypoxia occurred exclusively in the fluvial sections of the estuary during the high temperature and low river discharge period and was remarkably more serious in the river reach near the large urban area of Fuzhou. Enhancement of respiration by temperature and discharge of domestic sewage and industrial wastewater, versus regeneration of waters and dilution of pollutant concentration with increased river discharge, which regarded as the dominant antagonist processes that controlled the appearance of seasonal hypoxia. During the high temperature and the drought period, minimal mainstream flow above 700 m(3)Ÿs(-1), reduction of pollutants and forbidding sediment dredging in the South Channel should be guaranteed for strong supports on water quality management and drinking water source protection.