Difficult image segmentation problems, for instance left atrium MRI, can be addressed by incorporating shape priors to find solutions that are consistent with known objects. Nonetheless, a single multivariate Gaussian is not an adequate model in cases with significant nonlinear shape variation or where the prior distribution is multimodal. Nonparametric density estimation is more general, but has a ravenous appetite for training samples and poses serious challenges in optimization, especially in high dimensional spaces. Here, we propose a maximum-a-posteriori formulation that relies on a generative image model by incorporating both local intensity and global shape priors. We use deep autoencoders to capture the complex intensity distribution while avoiding the careful selection of hand-crafted features. We formulate the shape prior as a mixture of Gaussians and learn the corresponding parameters in a high-dimensional shape space rather than pre-projecting onto a low-dimensional subspace. In segmentation, we treat the identity of the mixture component as a latent variable and marginalize it within a generalized expectation-maximization framework. We present a conditional maximization-based scheme that alternates between a closed-form solution for component-specific shape parameters that provides a global update-based optimization strategy, and an intensity-based energy minimization that translates the global notion of a nonlinear shape prior into a set of local penalties. We demonstrate our approach on the left atrial segmentation from gadolinium-enhanced MRI, which is useful in quantifying the atrial geometry in patients with atrial fibrillation.

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.

In recent years, we have been faced with a series of natural disasters causing a tremendous amount of financial, environmental, and human losses. The unpredictable nature of natural disasters' behavior makes it hard to have a comprehensive situational awareness (SA) to support disaster management. Using opinion surveys is a traditional approach to analyze public concerns during natural disasters; however, this approach is limited, expensive, and time-consuming. Luckily the advent of social media has provided scholars with an alternative means of analyzing public concerns. Social media enable users (people) to freely communicate their opinions and disperse information regarding current events including natural disasters. This research emphasizes the value of social media analysis and proposes an analytical framework: Twitter Situational Awareness (TwiSA). This framework uses text mining methods including sentiment analysis and topic modeling to create a better SA for disaster preparedness, response, and recovery. TwiSA has also effectively deployed on a large number of tweets and tracks the negative concerns of people during the 2015 South Carolina flood.

Bayes' theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probabilities. This theorem has enormous importance in the field of data science. For example one of many applications of Bayes' theorem is the Bayesian inference, a particular approach to statistical inference. Bayesian inference is a method in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.

Bayes theorem in basis for many machine learning algorithm, P(c/x) P(x/c)*P(c)/P(x) Popularly used #Naive #Bayes Machine Learning algorithm is used for Text classification. One of the common question is "What is Bayes Theorem?" watch this video to understand this question and how to explain in the interview. If you are looking for Course Details please visit: https://datamites.com/ You can learn business statistics, tableau, deep learning, data mining etc,..

Novelty detection is the unsupervised problem of identifying anomalies in test data which significantly differ from the training set. Novelty detection is one of the classic challenges in Machine Learning and a core component of several research areas such as fraud detection, intrusion detection, medical diagnosis, data cleaning, and fault prevention. While numerous algorithms were designed to address this problem, most methods are only suitable to model continuous numerical data. Tackling datasets composed of mixed-type features, such as numerical and categorical data, or temporal datasets describing discrete event sequences is a challenging task. In addition to the supported data types, the key criteria for efficient novelty detection methods are the ability to accurately dissociate novelties from nominal samples, the interpretability, the scalability and the robustness to anomalies located in the training data. In this thesis, we investigate novel ways to tackle these issues. In particular, we propose (i) an experimental comparison of novelty detection methods for mixed-type data (ii) an experimental comparison of novelty detection methods for sequence data, (iii) a probabilistic nonparametric novelty detection method for mixed-type data based on Dirichlet process mixtures and exponential-family distributions and (iv) an autoencoder-based novelty detection model with encoder/decoder modelled as deep Gaussian processes.

Learning with noisy labels, which aims to reduce expensive labors on accurate annotations, has become imperative in the Big Data era. Previous noise transition based method has achieved promising results and presented a theoretical guarantee on performance in the case of class-conditional noise. However, this type of approaches critically depend on an accurate pre-estimation of the noise transition, which is usually impractical. Subsequent improvement adapts the pre-estimation along with the training progress via a Softmax layer. However, the parameters in the Softmax layer are highly tweaked for the fragile performance due to the ill-posed stochastic approximation. To address these issues, we propose a Latent Class-Conditional Noise model (LCCN) that naturally embeds the noise transition under a Bayesian framework. By projecting the noise transition into a Dirichlet-distributed space, the learning is constrained on a simplex based on the whole dataset, instead of some ad-hoc parametric space. We then deduce a dynamic label regression method for LCCN to iteratively infer the latent labels, to stochastically train the classifier and to model the noise. Our approach safeguards the bounded update of the noise transition, which avoids previous arbitrarily tuning via a batch of samples. We further generalize LCCN for open-set noisy labels and the semi-supervised setting. We perform extensive experiments with the controllable noise data sets, CIFAR-10 and CIFAR-100, and the agnostic noise data sets, Clothing1M and WebVision17. The experimental results have demonstrated that the proposed model outperforms several state-of-the-art methods.

A family of Markov blankets in a faithful Bayesian network satisfies the symmetry and consistency properties. In this paper, we draw a bijection between families of consistent Markov blankets and moral graphs. We define the new concepts of weak recursive simpliciality and perfect elimination kits. We prove that they are equivalent to graph morality. In addition, we prove that morality can be decided in polynomial time for graphs with maximum degree less than $5$, but the problem is NP-complete for graphs with higher maximum degrees.

Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account only the properties related to the intrinsic logical soundness of an argument in order to determine its acceptability status. However, these properties are not always the only ones that matter to establish the argument's acceptability---there exist other qualities, such as strength, weight, social votes, trust degree, relevance level, and certainty degree, among others.

Directed acyclic graph (DAG) models are popular for capturing causal relationships. From observational and interventional data, a DAG model can only be determined up to its \emph{interventional Markov equivalence class} (I-MEC). We investigate the size of MECs for random DAG models generated by uniformly sampling and ordering an Erd\H{o}s-R\'{e}nyi graph. For constant density, we show that the expected $\log$ observational MEC size asymptotically (in the number of vertices) approaches a constant. We characterize I-MEC size in a similar fashion in the above settings with high precision. We show that the asymptotic expected number of interventions required to fully identify a DAG is a constant. These results are obtained by exploiting Meek rules and coupling arguments to provide sharp upper and lower bounds on the asymptotic quantities, which are then calculated numerically up to high precision. Our results have important consequences for experimental design of interventions and the development of algorithms for causal inference.