We study the problem of modeling purchase of multiple items and utilizing it to display optimized recommendations, which is a central problem for online e-commerce platforms. Rich personalized modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the end user experience. We present a parsimonious multi-purchase family of choice models called the BundleMVL-K family, and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. This is one of the first attempts at operationalizing multi-purchase class of choice models. We characterize structural properties of the optimal solution, which allow one to decide if a product is part of the optimal assortment in constant time, reducing the size of the instance that needs to be solved computationally. We also establish the hardness of computing optimal recommendation sets. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. The benefit of taking multiple purchases into account is observed to be $6-8\%$ in relative terms for the Ta Feng and UCI shopping datasets when compared to the MNL model for instances with $\sim 1500$ products. Additionally, across $8$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale.

The article considers the problem of the optimal control of a wind power plant based on fuzzy control and automation of generating the fuzzy rule base. Fuzzy rules by experts do not always provide a maximum power output of the wind plant and fuzzy rule bases require an adjustment in the case of changing the parameters of the wind power plant or the environment. This research proposes the method for optimizing the fuzzy rules base compiled by various experts. The method is based on balancing weights of fuzzy rules into the base by the Particle Swarm Optimization algorithm. The experiment has shown that the proposed method allows forming the fuzzy rule base as an exemplary optimal base from a non-optimized set of fuzzy rules. The optimal fuzzy rule base has been taken under consideration for the concrete control loop of wind power plant and the concrete fuzzy model of the wind.

We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two individuals are connected by an edge independently from the other pairs and with a probability depending on their types. We consider here the dense case where the random network can be approximated by a graphon. This problem is motivated from the study of chain-referral surveys where each interviewee provides information on her/his contacts in the social network. First, we write the likelihood of the subgraph discovered by the random walk: biases are appearing since hubs and majority types are more likely to be sampled. Even for the case where the types are observed, the maximum likelihood estimator is not explicit any more. When the types of the vertices is unobserved, we use an SAEM algorithm to maximize the likelihood. Second, we propose a different estimation strategy using new results by Athreya and Roellin. It consists in de-biasing the maximum likelihood estimator proposed in Daudin et al. and that ignores the biases.

Rapid developments in data collecting devices and computation platforms produce an emerging number of learners and data modalities in many scientific domains. We consider the setting in which each learner holds a pair of parametric statistical model and a specific data source, with the goal of integrating information across a set of learners to enhance the prediction accuracy of a specific learner. One natural way to integrate information is to build a joint model across a set of learners that shares common parameters of interest. However, the parameter sharing patterns across a set of learners are not known a priori. Misspecifying the parameter sharing patterns and the parametric statistical model for each learner yields a biased estimator and degrades the prediction accuracy of the joint model. In this paper, we propose a novel framework for integrating information across a set of learners that is robust against model misspecification and misspecified parameter sharing patterns. The main crux is to sequentially incorporates additional learners that can enhance the prediction accuracy of an existing joint model based on a user-specified parameter sharing patterns across a set of learners, starting from a model with one learner. Theoretically, we show that the proposed method can data-adaptively select the correct parameter sharing patterns based on a user-specified parameter sharing patterns, and thus enhances the prediction accuracy of a learner. Extensive numerical studies are performed to evaluate the performance of the proposed method.

Digital twin technology has a huge potential for widespread applications in different industrial sectors such as infrastructure, aerospace, and automotive. However, practical adoptions of this technology have been slower, mainly due to a lack of application-specific details. Here we focus on a digital twin framework for linear single-degree-of-freedom structural dynamic systems evolving in two different operational time scales in addition to its intrinsic dynamic time-scale. Our approach strategically separates into two components -- (a) a physics-based nominal model for data processing and response predictions, and (b) a data-driven machine learning model for the time-evolution of the system parameters. The physics-based nominal model is system-specific and selected based on the problem under consideration. On the other hand, the data-driven machine learning model is generic. For tracking the multi-scale evolution of the system parameters, we propose to exploit a mixture of experts as the data-driven model. Within the mixture of experts model, Gaussian Process (GP) is used as the expert model. The primary idea is to let each expert track the evolution of the system parameters at a single time-scale. For learning the hyperparameters of the `mixture of experts using GP', an efficient framework the exploits expectation-maximization and sequential Monte Carlo sampler is used. Performance of the digital twin is illustrated on a multi-timescale dynamical system with stiffness and/or mass variations. The digital twin is found to be robust and yields reasonably accurate results. One exciting feature of the proposed digital twin is its capability to provide reasonable predictions at future time-steps. Aspects related to the data quality and data quantity are also investigated.

The continuous-time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, in social science models or in medicine. The literature on this topic is usually focused on the case when the dependence structure of a system is known and we are to determine conditional transition intensities (parameters of the network). In the paper, we study the structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes the dependence structure of the graph with high probability. We also investigate the properties of the procedure in numerical studies to demonstrate its effectiveness.

One of the most common statistical goals is to estimate a population parameter and quantify uncertainty by constructing a confidence interval. However, the field of differential privacy lacks easy-to-use and general methods for doing so. We partially fill this gap by developing two broadly applicable methods for private confidence-interval construction. The first is based on asymptotics: for two widely used model classes, exponential families and linear regression, a simple private estimator has the same asymptotic normal distribution as the corresponding non-private estimator, so confidence intervals can be constructed using quantiles of the normal distribution. These are computationally cheap and accurate for large data sets, but do not have good coverage for small data sets. The second approach is based on the parametric bootstrap. It applies "out of the box" to a wide class of private estimators and has good coverage at small sample sizes, but with increased computational cost. Both methods are based on post-processing the private estimator and do not consume additional privacy budget.

Many real-world situations allow for the acquisition of additional relevant information when making an assessment with limited or uncertain data. However, traditional ML approaches either require all features to be acquired beforehand or regard part of them as missing data that cannot be acquired. In this work, we propose models that dynamically acquire new features to further improve the prediction assessment. To trade off the improvement with the cost of acquisition, we leverage an information theoretic metric, conditional mutual information, to select the most informative feature to acquire. We leverage a generative model, arbitrary conditional flow (ACFlow), to learn the arbitrary conditional distributions required for estimating the information metric. We also learn a Bayesian network to accelerate the acquisition process. Our model demonstrates superior performance over baselines evaluated in multiple settings.

Latent position network models are a versatile tool in network science; applications include clustering entities, controlling for causal confounders, and defining priors over unobserved graphs. Estimating each node's latent position is typically framed as a Bayesian inference problem, with Metropolis within Gibbs being the most popular tool for approximating the posterior distribution. However, it is well-known that Metropolis within Gibbs is inefficient for large networks; the acceptance ratios are expensive to compute, and the resultant posterior draws are highly correlated. In this article, we propose an alternative Markov chain Monte Carlo strategy---defined using a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo---that leverages the posterior distribution's functional form for more efficient posterior computation. We demonstrate that these strategies outperform Metropolis within Gibbs and other algorithms on synthetic networks, as well as on real information-sharing networks of teachers and staff in a school district.

This paper extends the horseshoe prior of Carvalho et al. (2010) to the Bayesian quantile regression (HS-BQR) and provides a fast sampling algorithm that speeds up computation significantly in high dimensions. The performance of the HS-BQR is tested on large scale Monte Carlo simulations and an empirical application relevant to macroeoncomics. The Monte Carlo design considers several sparsity structures (sparse, dense, block) and error structures (i.i.d. errors and heteroskedastic errors). A number of LASSO based estimators (frequentist and Bayesian) are pitted against the HS-BQR to better gauge the performance of the method on the different designs. The HS-BQR yields just as good, or better performance than the other estimators considered when evaluated using coefficient bias and forecast error. We find that the HS-BQR is particularly potent in sparse designs and when estimating extreme quantiles. The simulations also highlight how the high dimensional quantile estimators fail to correctly identify the quantile function of the variables when both location and scale effects are present. In the empirical application, in which we evaluate forecast densities of US inflation, the HS-BQR provides well calibrated forecast densities whose individual quantiles, have the highest pseudo R squared, highlighting its potential for Value-at-Risk estimation.