Latent feature modeling allows capturing the latent structure responsible for generating the observed properties of a set of objects. It is often used to make predictions either for new values of interest or missing information in the original data, as well as to perform data exploratory analysis. However, although there is an extensive literature on latent feature models for homogeneous datasets, where all the attributes that describe each object are of the same (continuous or discrete) nature, there is a lack of work on latent feature modeling for heterogeneous databases. In this paper, we introduce a general Bayesian nonparametric latent feature model suitable for heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. First, it accounts for heterogeneous data while keeping the properties of conjugate models, which allow us to infer the model in linear time with respect to the number of objects and attributes. Second, its Bayesian nonparametric nature allows us to automatically infer the model complexity from the data, i.e., the number of features necessary to capture the latent structure in the data. Third, the latent features in the model are binary-valued variables, easing the interpretability of the obtained latent features in data exploratory analysis. We show the flexibility of the proposed model by solving both prediction and data analysis tasks on several real-world datasets. Moreover, a software package of the GLFM is publicly available for other researcher to use and improve it.

Bayes Nets (or Bayesian Networks) give remarkable results in determining the effects of many variables on an outcome. They typically perform strongly even in cases when other methods falter or fail. These networks have had relatively little use with business-related problems, although they have worked successfully for years in fields such as scientific research, public safety, aircraft guidance systems and national defense. Importantly, they often outperform regression, particularly in determining variables' effects. Regression is one of the most august multivariate methods, and among the most studied and applied.

One more opportunity to implement data mining techniques in the health care industry will be helping the healthcare insurers to detect fraud transactions so that the other patients can receive better and more affordable healthcare services. This occurs when individuals deceive an insurance company to try to obtain money to which they are not entitled. It happens when someone puts false information on an insurance application and when false or misleading information is given or important information is omitted in an insurance transaction or claim. Apart from the data we have collected from the patients, we will be gathering one more dataset where we will be having the details of all hospitals in the locality, diagnosis, quality. Evaluation: Here we cannot accurately classify whether a transaction is default or not, because of the challenges faced while collecting the data related to the hospitals.

Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dimensions. In particular we demonstrate that short-range Restricted Boltzmann Machines are Entangled Plaquette States, while fully connected Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of Restricted Boltzmann Machines and their efficiency at representing many-body quantum states. String-Bond States also provide a generic way of enhancing the power of Neural-Network Quantum States and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of Tensor Networks and the efficiency of Neural-Network Quantum States into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional Tensor Networks, we show that Neural-Network Quantum States and their String-Bond States extension can describe a lattice Fractional Quantum Hall state exactly. In addition, we provide numerical evidence that Neural-Network Quantum States can approximate a chiral spin liquid with better accuracy than Entangled Plaquette States and local String-Bond States. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.

We present a model that can automatically learn alignments between high-dimensional data in an unsupervised manner. Learning alignments is an ill-constrained problem as there are many different ways of defining a good alignment. Our proposed method casts alignment learning in a framework where both alignment and data are modelled simultaneously. We derive a probabilistic model built on non-parametric priors that allows for flexible warps while at the same time providing means to specify interpretable constraints. We show results on several datasets, including different motion capture sequences and show that the suggested model outperform the classical algorithmic approaches to the alignment task.

We show that the Ising distribution can be treated as a latent variable model, where a set of N real-valued, correlated random variables are drawn and used to generate N binary spins independently. This allows to approximate the Ising distribution by a simpler model where the latent variables follow a multivariate normal distribution. The resulting approximation bears similarities with the Thouless Anderson Palmer (TAP) solution from mean field theory, but retains a broader range of applicability when the coupling weights are not independently distributed. Moreover, unlike classic mean field approaches, the approximation can be used to generate correlated spin patterns.

For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this paper, we propose fast subsampling algorithms to efficiently approximate the maximum likelihood estimate in logistic regression. We first establish consistency and asymptotic normality of the estimator from a general subsampling algorithm, and then derive optimal subsampling probabilities that minimize the asymptotic mean squared error of the resultant estimator. An alternative minimization criterion is also proposed to further reduce the computational cost. The optimal subsampling probabilities depend on the full data estimate, so we develop a two-step algorithm to approximate the optimal subsampling procedure. This algorithm is computationally efficient and has a significant reduction in computing time compared to the full data approach. Consistency and asymptotic normality of the estimator from a two-step algorithm are also established. Synthetic and real data sets are used to evaluate the practical performance of the proposed method.

We propose a novel online learning algorithm for Restricted Boltzmann Machines (RBM), namely, the Online Generative Discriminative Restricted Boltzmann Machine (OGD-RBM), that provides the ability to build and adapt the network architecture of RBM according to the statistics of streaming data. The OGD-RBM is trained in two phases: (1) an online generative phase for unsupervised feature representation at the hidden layer and (2) a discriminative phase for classification. The online generative training begins with zero neurons in the hidden layer, adds and updates the neurons to adapt to statistics of streaming data in a single pass unsupervised manner, resulting in a feature representation best suited to the data. The discriminative phase is based on stochastic gradient descent and associates the represented features to the class labels. We demonstrate the OGD-RBM on a set of multi-category and binary classification problems for data sets having varying degrees of class-imbalance. We first apply the OGD-RBM algorithm on the multi-class MNIST dataset to characterize the network evolution. We demonstrate that the online generative phase converges to a stable, concise network architecture, wherein individual neurons are inherently discriminative to the class labels despite unsupervised training. We then benchmark OGD-RBM performance to other machine learning, neural network and ClassRBM techniques for credit scoring applications using 3 public non-stationary two-class credit datasets with varying degrees of class-imbalance. We report that OGD-RBM improves accuracy by 2.5-3% over batch learning techniques while requiring at least 24%-70% fewer neurons and fewer training samples. This online generative training approach can be extended greedily to multiple layers for training Deep Belief Networks in non-stationary data mining applications without the need for a priori fixed architectures.

Many applications of Bayesian data analysis involve sensitive information, motivating methods which ensure that privacy is protected. We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method. Our framework respects differential privacy, the gold-standard privacy criterion, and encompasses a large class of probabilistic models, called the Conjugate Exponential (CE) family. We observe that we can straightforwardly privatise VB's approximate posterior distributions for models in the CE family, by perturbing the expected sufficient statistics of the complete-data likelihood. For a broadly-used class of non-CE models, those with binomial likelihoods, we show how to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible, using the Polya-Gamma data augmentation scheme. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets.

The problem of reinforcement learning in an unknown and discrete Markov Decision Process (MDP) under the average-reward criterion is considered, when the learner interacts with the system in a single stream of observations, starting from an initial state without any reset. We revisit the minimax lower bound for that problem by making appear the local variance of the bias function in place of the diameter of the MDP. Furthermore, we provide a novel analysis of the KL-UCRL algorithm establishing a high-probability regret bound scaling as $\widetilde {\mathcal O}\Bigl({\textstyle \sqrt{S\sum_{s,a}{\bf V}^\star_{s,a}T}}\Big)$ for this algorithm for ergodic MDPs, where $S$ denotes the number of states and where ${\bf V}^\star_{s,a}$ is the variance of the bias function with respect to the next-state distribution following action $a$ in state $s$. The resulting bound improves upon the best previously known regret bound $\widetilde {\mathcal O}(DS\sqrt{AT})$ for that algorithm, where $A$ and $D$ respectively denote the maximum number of actions (per state) and the diameter of MDP. We finally compare the leading terms of the two bounds in some benchmark MDPs indicating that the derived bound can provide an order of magnitude improvement in some cases. Our analysis leverages novel variations of the transportation lemma combined with Kullback-Leibler concentration inequalities, that we believe to be of independent interest.