MS-MDA: Multisource Marginal Distribution Adaptation for Cross-Subject and Cross-Session EEG Emotion Recognition

As an essential element for the diagnosis and rehabilitation of psychiatric disorders, the electroencephalogram (EEG) based emotion recognition has achieved significant progress due to its high precision and reliability. However, one obstacle to practicality lies in the variability between subjects and sessions. Although several studies have adopted domain adaptation (DA) approaches to tackle this problem, most of them treat multiple EEG data from different subjects and sessions together as a single source domain for transfer, which either fails to satisfy the assumption of domain adaptation that the source has a certain marginal distribution, or increases the difficulty of adaptation. We therefore propose the multi-source marginal distribution adaptation (MS-MDA) for EEG emotion recognition, which takes both domain-invariant and domain-specific features into consideration. First, we assume that different EEG data share the same low-level features, then we construct independent branches for multiple EEG data source domains to adopt one-to-one domain adaptation and extract domain-specific features. Finally, the inference is made by multiple branches. We evaluate our method on SEED and SEED-IV for recognizing three and four emotions, respectively. Experimental results show that the MS-MDA outperforms the comparison methods and state-of-the-art models in cross-session and cross-subject transfer scenarios in our settings. Codes at https://github.com/VoiceBeer/MS-MDA.

Cheating with Models

Beliefs and decisions are often based on confronting models with data. What is the largest “fake” correlation that a misspecified model can generate, even when it passes an elementary misspecification test? We study an “analyst” who fits a model, represented by a directed acyclic graph, to an objective (multivariate) Gaussian distribution. We characterize the maximal estimated pairwise correlation for generic Gaussian objective distributions, subject to the constraint that the estimated model preserves the marginal distribution of any individual variable. As the number of model variables grows, the estimated correlation can become arbitrarily close to one regardless of the objective correlation. (JEL D83, C13, C46, C51)

Seismic fragility models of a bridge system based on copula method

Seismic fragility assessment widely uses a probabilistic measure for assessing the seismic performance of structural components or systems. This article proposes a copula-based seismic fragility (CBSF) method to derive the system-level damage probabilities of reinforced concrete bridges and to consider the correlation among seismic demands of components. First, the marginal distribution functions of the random variables are calibrated, and three Archimedean copula models are considered. Subsequently, the relevant parameters of the copula models are estimated using the semi-parametric maximum likelihood method. Next, the damage probabilities of a bridge system are calculated based on the joint distribution model with the most suitable copula model and the calibrated marginal distribution functions. Finally, the CBSF method is used to estimate the damage probability of a simply supported box girder bridge. The performance of the CBSF method is validated by a comparison of fragility curves obtained using the CBSF method and the probabilistic seismic demand analysis (PSDA) method. The comparative results demonstrate that the fragility curves obtained by the CBSF method are better than those obtained using the PSDA method. The proposed CBSF model can serve as a tool for assessing the seismic performance of structures and estimating the economic loss of existing bridge systems.

An intelligent fault diagnosis method for rolling bearings based on feature transfer with improved DenseNet and joint distribution adaptation

Mechanical intelligent fault diagnosis is an important method to accurately identify the health status of mechanical equipment. Traditional fault diagnosis methods perform poorly in the diagnosis of rolling bearings under complex conditions. In this paper, a feature transfer learning model based on improved DenseNet and joint distribution adaptation (FT-IDJ) is proposed. With this model, we apply it to implement rolling bearing fault diagnosis. A lightweight DenseNet model is firstly proposed to extract the transferable features of the raw vibration signal. Furthermore, the parameters in the DenseNet are constrained by the domain adaptive regularization term and pseudo label learning. The marginal distribution discrepancy and the conditional distribution discrepancy of the learned transferable features are reduced by this way. The proposed method is validated by the diagnosis experiments with CWRU and Jiangnan University rolling bearing datasets. The experimental results showed that the proposed FT-IDJ has higher classification accuracy than DAN and other eight methods, which demonstrated its effectively learning transferable features from auxiliary data.

SESR-based Identification of Flash Drought and Multivariate Drought Risk Probability Assessment in the Pearl River Basin, China

Flash drought (FD) is characterized by the rapid onset and development of drought conditions. It usually occurs during the growing seasons, causing more severe impacts on agriculture and society than the slowly-evolving droughts. Based on the Standard Evaporative Stress Ratio (SESR), this study presents an assessment of the spatio-temporal variability of the joint return periods of FD characteristics in the Pearl River basin (PRB), southern China. Three FD characteristics (i.e., duration D, intensity I, peak P) are extracted at each 0.25o×0.25o grid point over the PRB by the Runs theory. Four marginal distribution functions (Gamma, Exponential, Generalized Extreme Value and Lognormal) are used to fit FD characteristics, while three Archimedean Copula functions (Clayton, Frank and Gumbel) are used for generating the joint distributions of various paired FD characteristics. The results indicate that Lognormal is the best-fitted marginal distribution function of FD characteristics in most parts of PRB, while Frank and Clayton are the best-fitted Copula of the joint PDFs of three pairs of FD characteristics in most parts of PRB. During 1953–2013, the FD events are more frequent in eastern PRB (> 40 events) than western PRB (<10 events), and larger FD characteristics (D and I) are also found in eastern PRB than western PRB. The return period of each FD characteristic is smaller in eastern PRB than western PRB, leading to smaller joint return periods of three paired FD characteristics (D-I, D-P, P-I) in eastern PRB than western PRB. Overall, our results suggest that the risk of FD is gradually increased from the west to the east of the PRB.

Spatial Hurst–Kolmogorov Clustering

The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.

Identification of Epileptic EEG Signals Through TSK Transfer Learning Fuzzy System

We propose a new model to identify epilepsy EEG signals. Some existing intelligent recognition technologies require that the training set and test set have the same distribution when recognizing EEG signals, some only consider reducing the marginal distribution distance of the data while ignoring the intra-class information of data, and some lack of interpretability. To address these deficiencies, we construct a TSK transfer learning fuzzy system (TSK-TL) based on the easy-to-interpret TSK fuzzy system the transfer learning method. The proposed model is interpretable. By using the information contained in the source domain and target domains more effectively, the requirements for data distribution are further relaxed. It realizes the identification of epilepsy EEG signals in data drift scene. The experimental results show that compared with the existing algorithms, TSK-TL has better performance in EEG recognition of epilepsy.

Towards Generic Simulation for Demanding Stochastic Processes

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

Sweeps in time: leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome.

Bivariate Frequency of Meteorological Drought in the Upper Minjiang River Based on Copula Function

Based on the Standardized Precipitation Index (SPI) and copula function, this study analyzed the meteorological drought in the upper Minjiang River basin. The Tyson polygon method is used to divide the research area into four regions based on four meteorological stations. The monthly precipitation data of four meteorological stations from 1966 to 2016 were used for the calculation of SPI. The change trend of SPI1, SPI3 and SPI12 showed the historical dry-wet evolution phenomenon of short-term humidification and long-term aridification in the study area. The major drought events in each region are counted based on SPI3. The results show that the drought lasted the longest in Maoxian region, the occurrence of minor drought events was more frequent than the other regions. Nine distribution functions are used to fit the marginal distribution of drought duration (D), severity (S) and peak (P) estimated based on SPI3, the best marginal distribution is obtained by chi-square test. Five copula functions are used to create a bivariate joint probability distribution, the best copula function is selected through AIC, the univariate and bivariate return periods were calculated. The results of this paper will help the study area to assess the drought risk.