Nowadays, there are numerous risks related to bank loans both for the banks and the borrowers getting the loans. The risk analysis about bank loans needs understanding about the risk and the risk level. Banks need to analyze their customers for loan eligibility so that they can specifically target those customers. Banks wanted to automate the loan eligibility process (real time) based on customer details such as Gender, Marital Status, Age, Occupation, Income, debts, and others provided in their online application form. As the number of transactions in banking sector is rapidly growing and huge data volumes are available, the customers' behavior can be easily analyzed and the risks around loan can be reduced.

These days the terms "AI", "Machine Learning", "Deep Learning" are thrown around by companies in every industry, they're the type of words that make any forward-looking executive salivate. You might think these are new concepts that seemed to have appeared overnight, but the reality is they've been around for a while and it's the hard work of many within the field that has really moved it into the spotlight as the latest tech trend. While these terms are sometimes used interchangeably by the media they certainly are not the same, but I'll leave that discussion for another time. It's surely an exciting time for the industry, from a slew of open source libraries (TenserFlow, PredictionIO, DeepLearning4J, or see github) coming into popularity and every cloud provider from Amazon, IBM, Microsoft (the list goes on) all offering their own tools to help get started in the AI/ML/DL field. If you've stumbled on this article, you're probably well aware of everything I've mentioned above, so now that we've gotten past the obligatory intro, let's get to what the title actually claims this article is about.

We consider a decision-making problem where the environment varies both in space and time. Such problems arise naturally when considering e.g., the navigation of an underwater robot amidst ocean currents or the navigation of an aerial vehicle in wind. To model such spatiotemporal variation, we extend the standard Markov Decision Process (MDP) to a new framework called the Time-Varying Markov Decision Process (TVMDP). The TVMDP has a time-varying state transition model and transforms the standard MDP that considers only immediate and static uncertainty descriptions of state transitions, to a framework that is able to adapt to future time-varying transition dynamics over some horizon. We show how to solve a TVMDP via a redesign of the MDP value propagation mechanisms by incorporating the introduced dynamics along the temporal dimension. We validate our framework in a marine robotics navigation setting using spatiotemporal ocean data and show that it outperforms prior efforts.

Independent component analysis (ICA) is a widely used BSS method that can uniquely achieve source recovery, subject to only scaling and permutation ambiguities, through the assumption of statistical independence on the part of the latent sources. Independent vector analysis (IVA) extends the applicability of ICA by jointly decomposing multiple datasets through the exploitation of the dependencies across datasets. Though both ICA and IVA algorithms cast in the maximum likelihood (ML) framework enable the use of all available statistical information in reality, they often deviate from their theoretical optimality properties due to improper estimation of the probability density function (PDF). This motivates the development of flexible ICA and IVA algorithms that closely adhere to the underlying statistical description of the data. Although it is attractive minimize the assumptions, important prior information about the data, such as sparsity, is usually available. If incorporated into the ICA model, use of this additional information can relax the independence assumption, resulting in an improvement in the overall separation performance. Therefore, the development of a unified mathematical framework that can take into account both statistical independence and sparsity is of great interest. In this work, we first introduce a flexible ICA algorithm that uses an effective PDF estimator to accurately capture the underlying statistical properties of the data. We then discuss several techniques to accurately estimate the parameters of the multivariate generalized Gaussian distribution, and how to integrate them into the IVA model. Finally, we provide a mathematical framework that enables direct control over the influence of statistical independence and sparsity, and use this framework to develop an effective ICA algorithm that can jointly exploit these two forms of diversity.

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$ enables the solution to many problems in machine learning (e.g. Bayesian inference, generative modeling) and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations , in general, still comprises computational difficulties, especially in high dimensions. Here, we consider the problem of computing such "measure transport maps" with efficient and parallelizable methods. Under the mild assumptions that $P$ need not be known but can be sampled from, that the density of $Q$ is known up to a proportionality constant, and that $Q$ is log-concave, we provide a convex optimization problem pertaining to relative entropy minimization. We show how an empirical minimization formulation and polynomial chaos map parameterization can allow for learning a transport map between $P$ and $Q$ with distributed and scalable methods. We also leverage findings from nonequilibrium thermodynamics to represent the transport map as a composition of simpler maps, each of which is learned sequentially with a transport cost regularized version of the aforementioned problem formulation. We provide examples of our framework within the context of Bayesian inference for the Boston housing dataset, active learning for optimizing human computer interfaces, density estimation for probabilistic sleep staging with EEG, and generative modeling for handwritten digit images from the MNIST dataset.

We consider the problem of estimating a large rank-one tensor ${\boldsymbol u}^{\otimes k}\in({\mathbb R}^{n})^{\otimes k}$, $k\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\lambda\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\ll \lambda\ll n^{(k-2)/4}$. In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-$k$ homogeneous polynomial over the unit sphere in $n$ dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions $n$, and give exact formulas for the exponential growth rate. We show that (for $\lambda$ larger than a constant) critical points are either very close to the unknown vector ${\boldsymbol u}$, or are confined in a band of width $\Theta(\lambda^{-1/(k-1)})$ around the maximum circle that is orthogonal to ${\boldsymbol u}$. For local maxima, this band shrinks to be of size $\Theta(\lambda^{-1/(k-2)})$. These `uninformative' local maxima are likely to cause the failure of optimization algorithms.

We introduce a new family of MCMC samplers that combine auxiliary variables, Gibbs sampling and Taylor expansions of the target density. Our approach permits the marginalisation over the auxiliary variables yielding marginal samplers, or the augmentation of the auxiliary variables, yielding auxiliary samplers. The well-known Metropolis-adjusted Langevin algorithm (MALA) and preconditioned Crank-Nicolson Langevin (pCNL) algorithm are shown to be special cases. We prove that marginal samplers are superior in terms of asymptotic variance and demonstrate cases where they are slower in computing time compared to auxiliary samplers. In the context of latent Gaussian models we propose new auxiliary and marginal samplers whose implementation requires a single tuning parameter, which can be found automatically during the transient phase. Extensive experimentation shows that the increase in efficiency (measured as effective sample size per unit of computing time) relative to (optimised implementations of) pCNL, elliptical slice sampling and MALA ranges from 10-fold in binary classification problems to 25-fold in log-Gaussian Cox processes to 100-fold in Gaussian process regression, and it is on par with Riemann manifold Hamiltonian Monte Carlo in an example where the latter has the same complexity as the aforementioned algorithms. We explain this remarkable improvement in terms of the way alternative samplers try to approximate the eigenvalues of the target. We introduce a novel MCMC sampling scheme for hyperparameter learning that builds upon the auxiliary samplers. The MATLAB code for reproducing the experiments in the article is publicly available and a Supplement to this article contains additional experiments and implementation details.

In this paper, we design a nonparametric online algorithm for estimating the triggering functions of multivariate Hawkes processes. Unlike parametric estimation, where evolutionary dynamics can be exploited for fast computation of the gradient, and unlike typical function learning, where representer theorem is readily applicable upon proper regularization of the objective function, nonparametric estimation faces the challenges of (i) inefficient evaluation of the gradient, (ii) lack of representer theorem, and (iii) computationally expensive projection necessary to guarantee positivity of the triggering functions. In this paper, we offer solutions to the above challenges, and design an online estimation algorithm named NPOLE-MHP that outputs estimations with a $\mathcal{O}(1/T)$ regret, and a $\mathcal{O}(1/T)$ stability. Furthermore, we design an algorithm, NPOLE-MMHP, for estimation of multivariate marked Hawkes processes. We test the performance of NPOLE-MHP on various synthetic and real datasets, and demonstrate, under different evaluation metrics, that NPOLE-MHP performs as good as the optimal maximum likelihood estimation (MLE), while having a run time as little as parametric online algorithms.

Our article considers variational approximations of the posterior distribution in a high-dimensional state space model. The variational approximation is a multivariate Gaussian density, in which the variational parameters to be optimized are a mean vector and a covariance matrix. The number of parameters in the covariance matrix grows as the square of the number of model parameters, so it is necessary to find simple yet effective parametrizations of the covariance structure when the number of model parameters is large. The joint posterior distribution over the high-dimensional state vectors is approximated using a dynamic factor model, with Markovian dependence in time and a factor covariance structure for the states. This gives a reduced dimension description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. We illustrate our approach in two high-dimensional applications which are challenging for Markov chain Monte Carlo sampling. The first is a spatio-temporal model for the spread of the Eurasian Collared-Dove across North America. The second is a multivariate stochastic volatility model for financial returns via a Wishart process.

Consider a multi-variate time series $(X_t)_{t=0}^{T}$ where $X_t \in \mathbb{R}^d$ which may represent spike train responses for multiple neurons in a brain, crime event data across multiple regions, and many others. An important challenge associated with these time series models is to estimate an influence network between the $d$ variables, especially when the number of variables $d$ is large meaning we are in the high-dimensional setting. Prior work has focused on parametric vector auto-regressive models. However, parametric approaches are somewhat restrictive in practice. In this paper, we use the non-parametric sparse additive model (SpAM) framework to address this challenge. Using a combination of $\beta$ and $\phi$-mixing properties of Markov chains and empirical process techniques for reproducing kernel Hilbert spaces (RKHSs), we provide upper bounds on mean-squared error in terms of the sparsity $s$, logarithm of the dimension $\log d$, number of time points $T$, and the smoothness of the RKHSs. Our rates are sharp up to logarithm factors in many cases. We also provide numerical experiments that support our theoretical results and display potential advantages of using our non-parametric SpAM framework for a Chicago crime dataset.