Interviewing is a grueling process, specially during COVID. I recently interviewed with Microsoft (Data Scientist ll), Amazon (Applied AI Scientist) and Apple (Software Development : Machine…

Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a sufficiently flexible and statistically reliable way within a unifying asset pricing framework. Consequently, little is known empirically about the expected risk-premia of CAT bonds. The primary contribution of this paper is to present a unified Bayesian CAT bond pricing framework based on uncertainty quantification of catastrophes and interest rates. Our framework allows for complex beliefs about catastrophe risks to capture the distinct and common patterns in catastrophe occurrences, and when combined with stochastic interest rates, yields a unified asset pricing approach with informative expected risk premia. Specifically, using a modified collective risk model -- Dirichlet Prior-Hierarchical Bayesian Collective Risk Model (DP-HBCRM) framework -- we model catastrophe risk via a model-based clustering approach. Interest rate risk is modeled as a CIR process under the Bayesian approach. As a consequence of casting CAT pricing models into our framework, we evaluate the price and expected risk premia of various CAT bond contracts corresponding to clustering of catastrophe risk profiles. Numerical experiments show how these clusters reveal how CAT bond prices and expected risk premia relate to claim frequency and loss severity.

As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It has been pointed out in the literature that the difficulty of high-dimensional classification problems is intrinsically caused by too many noise variables useless for reducing classification error, which offer less benefits for decision-making, and increase complexity, and confusion in model-interpretation. A good variable selection strategy is therefore a must for using such kinds of data well; especially when we expect to use their results for the succeeding applications/studies, where the model-interpretation ability is essential. hus, the conventional classification measures, such as accuracy, sensitivity, precision, cannot be the only performance tasks. In this paper, we propose a probability-based nonparametric multiple-class classification method, and integrate it with the ability of identifying high impact variables for individual class such that we can have more information about its classification rule and the character of each class as well. The proposed method can have its prediction power approximately equal to that of the Bayes rule, and still retains the ability of "model-interpretation." We report the asymptotic properties of the proposed method, and use both synthesized and real data sets to illustrate its properties under different classification situations. We also separately discuss the variable identification, and training sample size determination, and summarize those procedures as algorithms such that users can easily implement them with different computing languages.

This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into predictive models. We consider the probabilistic learning of a random vector that is made up of either a quantity of interest (unsupervised case) or the couple of the quantity of interest and a control parameter (supervised case). A training set of independent realizations of this random vector is assumed to be given and to be generated with a prior probability measure that is unknown. A target set of realizations of the QoI is available for the two considered cases. The framework is the one of non-Gaussian problems in high dimension. A functional approach is developed on the basis of a weak formulation of the Fourier transform of probability measures (characteristic functions). The construction makes it possible to take into account the target set of realizations of the QoI in the Kullback-Leibler minimum principle. The proposed approach allows for estimating the posterior probability measure of the QoI (unsupervised case) or of the posterior joint probability measure of the QoI with the control parameter (supervised case). The existence and the uniqueness of the posterior probability measure is analyzed for the two cases. The numerical aspects are detailed in order to facilitate the implementation of the proposed method. The presented application in high dimension demonstrates the efficiency and the robustness of the proposed algorithm.

Deep reinforcement learning (DRL) has made significant achievements in many real-world applications. But these real-world applications typically can only provide partial observations for making decisions due to occlusions and noisy sensors. However, partial state observability can be used to hide malicious behaviors for backdoors. In this paper, we explore the sequential nature of DRL and propose a novel temporal-pattern backdoor attack to DRL, whose trigger is a set of temporal constraints on a sequence of observations rather than a single observation, and effect can be kept in a controllable duration rather than in the instant. We validate our proposed backdoor attack to a typical job scheduling task in cloud computing. Numerous experimental results show that our backdoor can achieve excellent effectiveness, stealthiness, and sustainability. Our backdoor's average clean data accuracy and attack success rate can reach 97.8% and 97.5%, respectively.

Describing the causal relations governing a system is a fundamental task in many scientific fields, ideally addressed by experimental studies. However, obtaining data under intervention scenarios may not always be feasible, while discovering causal relations from purely observational data is notoriously challenging. In certain settings, such as genomics, we may have data from heterogeneous study conditions, with soft (partial) interventions only pertaining to a subset of the study variables, whose effects and targets are possibly unknown. Combining data from experimental and observational studies offers the opportunity to leverage both domains and improve on the identifiability of causal structures. To this end, we define the interventional BGe score for a mixture of observational and interventional data, where the targets and effects of intervention may be unknown. To demonstrate the approach we compare its performance to other state-of-the-art algorithms, both in simulations and data analysis applications. Prerogative of our method is that it takes a Bayesian perspective leading to a full characterisation of the posterior distribution of the DAG structures. Given a sample of DAGs one can also automatically derive full posterior distributions of the intervention effects. Consequently the method effectively captures the uncertainty both in the structure and the parameter estimates. Codes to reproduce the simulations and analyses are publicly available at github.com/jackkuipers/iBGe

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Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks -- long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.

Natural processes may undergo transient periods of nonstationarity which produce lasting change in process behavior across time. When driven by exogeneous influences these changes can be challenging to predict in advance. To circumvent this challenge, works in online (sequential) change detection aim to deduce the occurrence of change in process behavior as it occurs via direct observation of an online data stream. While such changes in process behavior are most commonly modeled via change-points, in which the parameters and/or densities defining an associated process model are assumed to undergo an abrupt and instantaneous transition, changes in the behavior of some processes may occur gradually, taking time to reach their full effect. In such cases change-point models may be ill suited, producing either inaccurate estimates for the timing of these changes or, when this gradual change occurs slowly and when change detection is performed concurrently with model estimation, failing to properly detect change occurrence, as we show empirically in Section 4. This effect can have a significant impact in application, where automated system controls may not be appropriately applied at the correct times, and can result in inaccurate models of process behavior during and after this gradual change.

The Deep Q -Network (Mnih et al., 2015), as a typical example of Q -learning with function approximation, is one of the most successful algorithms to solve the reinforcement learning (RL) problem, and hence is viewed as a milestone in the development of modern RL. On the other hand, the behavior of Q -learning with function approximation is theoretically not well understood, and was identified in Sutton (1999) as one of four most important theoretical open problems. In fact, the infamous deadly triad (Sutton, 2015) is present in Q -learning with function approximation, and hence even in the basic setting where linear function approximation is used, the algorithm was shown to be unstable in general (Baird, 1995). While theoretically unclear, it was empirically evident from Mnih et al. (2015) that the following three ingredients: experience replay, target network, and truncation together overcome the divergence of Q - learning with function approximation. In this work, we focus on Q -learning with linear function approximation for infinite horizon discounted Markov decision processes (MDPs), and show theoretically that target network together with truncation is sufficient to provably stabilize Q -learning. The main contributions of this work are summarized in the following.