HSIC Regularized LTSA

Hilbert-Schmidt Independence Criterion (HSIC) measures statistical independence between two random variables. However, instead of measuring the statistical independence between two random variables directly, HSIC first transforms two random variables into two Reproducing Kernel Hilbert Spaces (RKHS) respectively and then measures the kernelled random variables by using Hilbert-Schmidt (HS) operators between the two RKHS. Since HSIC was first proposed around 2005, HSIC has found wide applications in machine learning. In this paper, a HSIC regularized Local Tangent Space Alignment algorithm (HSIC-LTSA) is proposed. LTSA is a well-known dimensionality reduction algorithm for local homeomorphism preservation. In HSIC-LTSA, behind the objective function of LTSA, HSIC between high-dimensional and dimension-reduced data is added as a regularization term. The proposed HSIC-LTSA has two contributions. First, HSIC-LTSA implements local homeomorphism preservation and global statistical correlation during dimensionality reduction. Secondly, HSIC-LTSA proposes a new way to apply HSIC: HSIC is used as a regularization term to be added to other machine learning algorithms. The experimental results presented in this paper show that HSIC-LTSA can achieve better performance than the original LTSA

Bid Optimization for Offsite Display Ad Campaigns on eCommerce

Online retailers often use third-party demand-side-platforms (DSPs) to conduct offsite advertising and reach shoppers across the Internet on behalf of their advertisers. The process involves the retailer participating in instant auctions with real-time bidding for each ad slot of their interest. In this paper, we introduce a bid optimization system that leverages the dimensional bidding function provided by most well-known DSPs for Walmart offsite display ad campaigns. The system starts by automatically searching for the optimal segmentation of the ad requests space based on their characteristics such as geo location, time, ad format, serving website, device type, etc. Then, it assesses the quality of impressions observed from each dimension based on revenue signals driven by the campaign effect. During the campaign, the system iteratively approximates the bid landscape based on the data observed and calculates the bid adjustments for each dimension. Finally, a higher bid adjustment factor is applied to dimensions with potentially higher revenue over ad spend (ROAS), and vice versa. The initial A/B test results of the proposed optimization system has shown its effectiveness of increasing the ROAS and conversion rate while reducing the effective cost per mille for ad serving

Change Point Detection on a Separable Model for Dynamic Networks

This paper studies the change point detection problem in time series of networks, with the Separable Temporal Exponential-family Random Graph Model (STERGM). We consider a sequence of networks generated from a piecewise constant distribution that is altered at unknown change points in time. Detection of the change points can identify the discrepancies in the underlying data generating processes and facilitate downstream dynamic network analysis tasks. Moreover, the STERGM that focuses on network statistics is a flexible model to fit dynamic networks with both dyadic and temporal dependence. We propose a new estimator derived from the Alternating Direction Method of Multipliers (ADMM) and the Group Fused Lasso to simultaneously detect multiple time points, where the parameters of STERGM have changed. We also provide Bayesian information criterion for model selection to assist the detection. Our experiments show good performance of the proposed method on both simulated and real data. Lastly, we develop an R package CPDstergm to implement our method

Structural Learning of Gaussian DAGs from Network Data

Structural learning of Gaussian directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. But in real applications such as in biology and social studies observations generated from a Bayesian network model are often mutually dependent and their dependence can be model by a second network model. In this dissertation, we generalize the existing Gaussian DAG framework by proposing a new Gaussian DAG model for dependent data which assumes the observations are correlated according to a given undirected network. Under this model, the dependent observations jointly follow a matrix normal distribution with variance represented by the Kronecker product of two positive definite matrices. The Cholesky factor of one of the matrices represent the DAG structure in the feature space while the other encodes the conditional independencies among the observations. We show that the proposed model also satisfies the desired score-equivalence property under common likelihood-based score functions. Based on the proposed model, we develop a block coordinate descent algorithm to estimate the DAG structure given a topological ordering of the vertices. The proposed algorithm jointly estimates a sparse Bayesian network and the correlations among observations by optimizing a scoring function based on penalized likelihood. The algorithm is fast and can scale to networks with thousands of nodes. We also established finite-sample error bounds and large-sample consistency of the estimators. In particular, we show that under some mild conditions, the proposed method produces consistent estimators for the DAG structure and the sample covariances after one iteration. Extensive numerical experiments also demonstrate that by jointly estimating the DAG structure and the sample correlation, our method achieves much higher accuracy in structure learning than the competing algorithms. When the node ordering is unknown, through experiments on synthetic and real data, we show that our algorithm can be used to estimate the correlations between samples, with which we can de-correlate the dependent data to significantly improve the performance of classical DAG learning methods

Structural Learning of Gaussian DAGs from Network Data

Structural learning of Gaussian directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. But in real applications such as in biology and social studies observations generated from a Bayesian network model are often mutually dependent and their dependence can be model by a second network model. In this dissertation, we generalize the existing Gaussian DAG framework by proposing a new Gaussian DAG model for dependent data which assumes the observations are correlated according to a given undirected network. Under this model, the dependent observations jointly follow a matrix normal distribution with variance represented by the Kronecker product of two positive definite matrices. The Cholesky factor of one of the matrices represent the DAG structure in the feature space while the other encodes the conditional independencies among the observations. We show that the proposed model also satisfies the desired score-equivalence property under common likelihood-based score functions. Based on the proposed model, we develop a block coordinate descent algorithm to estimate the DAG structure given a topological ordering of the vertices. The proposed algorithm jointly estimates a sparse Bayesian network and the correlations among observations by optimizing a scoring function based on penalized likelihood. The algorithm is fast and can scale to networks with thousands of nodes. We also established finite-sample error bounds and large-sample consistency of the estimators. In particular, we show that under some mild conditions, the proposed method produces consistent estimators for the DAG structure and the sample covariances after one iteration. Extensive numerical experiments also demonstrate that by jointly estimating the DAG structure and the sample correlation, our method achieves much higher accuracy in structure learning than the competing algorithms. When the node ordering is unknown, through experiments on synthetic and real data, we show that our algorithm can be used to estimate the correlations between samples, with which we can de-correlate the dependent data to significantly improve the performance of classical DAG learning methods

Real-time correction method of Muskingum model based on Kalman filter

In flood forecasting, general flood forecasting models or empirical forecasts reflect the average optimal value or relationship curve under the previous data. However, in the operation forecast, the forecast plan value often deviates from the actual situation. This paper takes Muskingum model as an example, and uses the Kalman filter algorithm to correct the forecast results. The algorithm structure and principles were described detailed, and the numerical simulation test was set to verify the efficiency of the Kalman filter algorithm. The correct results with corrected method were compared. The results indicated that the efficiency of the updating system using Kalman filter algorithm was improved. Conclusively, the proposed method could be widely applied in real-time flood forecast updating

Analysis of Time and Beam Synchronization Errors for Distributed Spaceborne SAR System

Synchronization is a key problem in distributed Synthetic Aperture Radar (SAR) systems. In this paper, we perform a complex mathematical deduction and then analyze the influences of time synchronization on the SAR imaging and interferometric process. We discuss the relationship between time and phase synchronization, considering that different oscillators in separated transmitters and receivers lead to both time and phase synchronization errors. With respect to beam synchronization, we present the effects of the accuracies of beam pointing and satellite attitude on the antenna gain, based on the attitude-steering strategy, which involves azimuth weighting of the Doppler spectra for independent zero-Doppler beam steering. We also analyze the influences of beam synchronization on Doppler decorrelation, Signal-to-Noise Ratio (SNR), and overlapping swath error. We conduct simulations to validate the analysis results. Our findings provide guidance for system design

Memristors based on amorphous ZnSnO films

Memristors based on amorphous ZnSnO film