Regulators require financial institutions to estimate counterparty default risks from liquid CDS quotes for the valuation and risk management of OTC derivatives. However, the vast majority of counterparties do not have liquid CDS quotes and need proxy CDS rates. Existing methods cannot account for counterparty-specific default risks; we propose to construct proxy CDS rates by associating to illiquid counterparty liquid CDS Proxy based on Machine Learning Techniques. After testing 156 classifiers from 8 most popular classifier families, we found that some classifiers achieve highly satisfactory accuracy rates. Furthermore, we have rank-ordered the performances and investigated performance variations amongst and within the 8 classifier families. This paper is, to the best of our knowledge, the first systematic study of CDS Proxy construction by Machine Learning techniques, and the first systematic classifier comparison study based entirely on financial market data. Its findings both confirm and contrast existing classifier performance literature. Given the typically highly correlated nature of financial data, we investigated the impact of correlation on classifier performance. The techniques used in this paper should be of interest for financial institutions seeking a CDS Proxy method, and can serve for proxy construction for other financial variables. Some directions for future research are indicated.

The Monty Hall problem was first featured on the classic game show "Let's make a Deal". In the final segment of the show, contestants were presented with a choice of three different doors. Behind two of the doors would be a goat, and behind the third would be an extravagant prize such as a car. The contestant begins the game by picking one door. The host, Monty Hall, would then open one of the remaining doors.

Fingerprinting based WLAN indoor positioning system (FWIPS) provides a promising indoor positioning solution to meet the growing interests for indoor location-based services (e.g., indoor way finding or geo-fencing). FWIPS is preferred because it requires no additional infrastructure for deploying an FWIPS and achieving the position estimation by reusing the available WLAN and mobile devices, and capable of providing absolute position estimation. For fingerprinting based positioning (FbP), a model is created to provide reference values of observable features (e.g., signal strength from access point (AP)) as a function of location during offline stage. One widely applied method to build a complete and an accurate reference database (i.e. radio map (RM)) for FWIPS is carrying out a site survey throughout the region of interest (RoI). Along the site survey, the readings of received signal strength (RSS) from all visible APs at each reference point (RP) are collected. This site survey, however, is time-consuming and labor-intensive, especially in the case that the RoI is large (e.g., an airport or a big mall). This bottleneck hinders the wide commercial applications of FWIPS (e.g., proximity promotions in a shopping center). To diminish the cost of site survey, we propose a probabilistic model, which combines fingerprinting based positioning (FbP) and RM generation based on stochastic variational Bayesian inference (SVBI). This SVBI based position and RSS estimation has three properties: i) being able to predict the distribution of the estimated position and RSS, ii) treating each observation of RSS at each RP as an example to learn for FbP and RM generation instead of using the whole RM as an example, and iii) requiring only one time training of the SVBI model for both localization and RSS estimation. These benefits make it outperforms the previous proposed approaches.

Non-impeding noisy-And Trees (NATs) provide a general, expressive, and efficient causal model for conditional probability tables (CPTs) in discrete Bayesian networks (BNs). A BN CPT may either be directly expressed as a NAT model or be compressed into one. Once CPTs in BNs are so expressed or compressed, complexity of inference (both space and time) can be significantly reduced. The most important operation in encoding or compressing CPTs into NAT models is extracting the NAT structure from interaction patterns between causes. The existing method does so by referencing a NAT database and an associated search tree. Although both are constructed offline, their complexity is exponential on the number of causes. In this work, we propose a novel method for NAT extraction from causal interaction patterns based on bipartition of causes. The method does not require the support of a NAT database and the related search tree, making NAT extraction more efficient and flexible.

A central task in discrete Bayesian network (BN) inference is to determine those variables relevant to answer a given query. Two linear algorithms for this task explore the possibly relevant and active parts of a BN, respectively. We empirically compare these two methods along with a variation of each.

A fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connectivity. The approach combines the tractability and flexibility of autoregressive modeling with the biophysical interpretability of dynamic causal modeling. The causal kernels are learned nonparametrically using Gaussian process regression, yielding an efficient framework for causal inference. We construct a novel class of causal covariance functions that enforce the desired properties of the causal kernels, an approach which we call GP CaKe. By construction, the model and its hyperparameters have biophysical meaning and are therefore easily interpretable. We demonstrate the efficacy of GP CaKe on a number of simulations and give an example of a realistic application on magnetoencephalography (MEG) data.

We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative logarithm of the prior probability density function). Our alternating direction method of multipliers (ADMM)-based approach translates the estimation task into successive applications of the proximal mapping of the penalty function. Capitalizing on this direct link, we define the proximal operator as a parametric spline curve and optimize the spline coefficients by minimizing the average reconstruction error for a given training set. The key aspects of our learning method are that the associated penalty function is constrained to be convex and the convergence of the ADMM iterations is proven. As a result of these theoretical guarantees, adaptation of the proposed framework to different levels of measurement noise is extremely simple and does not require any retraining. We apply our method to estimation of both sparse and non-sparse models of L\'{e}vy processes for which the minimum mean square error (MMSE) estimators are available. We carry out a single training session and perform comparisons at various signal-to-noise ratio (SNR) values. Simulations illustrate that the performance of our algorithm is practically identical to the one of the MMSE estimator irrespective of the noise power.

The Madrid ASDM summer school is in its twelfth edition this year, with hundreds of students from all over the world having attended so far. It comprises 12 intensive (15 lecture hours) week-long courses, and a student may attend from one up to six courses. The courses cover topics such as Neural Networks and Deep Learning, Bayesian Networks, Big Data with Apache Spark, Bayesian Inference, Text Mining and Time Series, and each has theoretical as well as practical classes, done with R or python. While the summer school is mainly attended by people from academia - PhD students and researchers, people from the industry also assist. The students come from diverse backgrounds, ranging from biology to economics to mathematics and physics.

In this post, we consider different approaches for time series modeling. The forecasting approaches using linear models, ARIMA alpgorithm, XGBoost machine learning algorithm are described. Results of different model combinations are shown. For probabilistic modeling the approaches using copulas and Bayesian inference are considered. Time series analysis, especially forecasting, is an important problem of modern predictive analytics.

A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, VB methods have emerged as a popular alternative to the classical MCMC methods. VB methods tend to be faster while achieving comparable predictive performance. However, there are few theoretical results around VB. In this paper, we establish frequentist consistency and asymptotic normality of VB methods. Specifically, we connect VB methods to point estimates based on variational approximations, called frequentist variational approximations, and we use the connection to prove a variational Bernstein-von-Mises theorem. The theorem leverages the theoretical characterizations of frequentist variational approximations to understand asymptotic properties of VB. In summary, we prove that (1) the VB posterior converges to the KL minimizer of a normal distribution, centered at the truth and (2) the corresponding variational expectation of the parameter is consistent and asymptotically normal. As applications of the theorem, we derive asymptotic properties of VB posteriors in Bayesian mixture models, Bayesian generalized linear mixed models, and Bayesian stochastic block models. We conduct a simulation study to illustrate these theoretical results.