Missing data and noisy observations pose significant challenges for reliably predicting events from irregularly sampled multivariate time series (longitudinal) data. Imputation methods, which are typically used for completing the data prior to event prediction, lack a principled mechanism to account for the uncertainty due to missingness. Alternatively, state-of-the-art joint modeling techniques can be used for jointly modeling the longitudinal and event data and compute event probabilities conditioned on the longitudinal observations. These approaches, however, make strong parametric assumptions and do not easily scale to multivariate signals with many observations. Our proposed approach consists of several key innovations. First, we develop a flexible and scalable joint model based upon sparse multiple-output Gaussian processes. Unlike state-of-the-art joint models, the proposed model can explain highly challenging structure including non-Gaussian noise while scaling to large data. Second, we derive an optimal policy for predicting events using the distribution of the event occurrence estimated by the joint model. The derived policy trades-off the cost of a delayed detection versus incorrect assessments and abstains from making decisions when the estimated event probability does not satisfy the derived confidence criteria. Experiments on a large dataset show that the proposed framework significantly outperforms state-of-the-art techniques in event prediction.

There has been a growing interest in using nonparametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally intensive, (2) it cannot efficiently implement newly obtained measurements online, and (3) it cannot deal with stochastic (noisy) input points. In this paper we present an algorithm tackling all these three issues simultaneously. The resulting Sparse Online Noisy Input GP (SONIG) regression algorithm can incorporate new noisy measurements in constant runtime. A comparison has shown that it is more accurate than similar existing regression algorithms. When applied to nonlinear black-box system modeling, its performance is competitive with existing nonlinear ARX models. Keywords: Nonlinear system identification, Gaussian processes, regression, machine learning, sparse methods.

Topic models, and more specifically the class of Latent Dirichlet Allocation (LDA), are widely used for probabilistic modeling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler.

Accurately predicting the time of occurrence of an event of interest is a critical problem in longitudinal data analysis. One of the main challenges in this context is the presence of instances whose event outcomes become unobservable after a certain time point or when some instances do not experience any event during the monitoring period. Such a phenomenon is called censoring which can be effectively handled using survival analysis techniques. Traditionally, statistical approaches have been widely developed in the literature to overcome this censoring issue. In addition, many machine learning algorithms are adapted to effectively handle survival data and tackle other challenging problems that arise in real-world data. In this survey, we provide a comprehensive and structured review of the representative statistical methods along with the machine learning techniques used in survival analysis and provide a detailed taxonomy of the existing methods. We also discuss several topics that are closely related to survival analysis and illustrate several successful applications in various real-world application domains. We hope that this paper will provide a more thorough understanding of the recent advances in survival analysis and offer some guidelines on applying these approaches to solve new problems that arise in applications with censored data.

Fuzzy controllers are efficient and interpretable system controllers for continuous state and action spaces. To date, such controllers have been constructed manually or trained automatically either using expert-generated problem-specific cost functions or incorporating detailed knowledge about the optimal control strategy. Both requirements for automatic training processes are not found in most real-world reinforcement learning (RL) problems. In such applications, online learning is often prohibited for safety reasons because online learning requires exploration of the problem's dynamics during policy training. We introduce a fuzzy particle swarm reinforcement learning (FPSRL) approach that can construct fuzzy RL policies solely by training parameters on world models that simulate real system dynamics. These world models are created by employing an autonomous machine learning technique that uses previously generated transition samples of a real system. To the best of our knowledge, this approach is the first to relate self-organizing fuzzy controllers to model-based batch RL. Therefore, FPSRL is intended to solve problems in domains where online learning is prohibited, system dynamics are relatively easy to model from previously generated default policy transition samples, and it is expected that a relatively easily interpretable control policy exists. The efficiency of the proposed approach with problems from such domains is demonstrated using three standard RL benchmarks, i.e., mountain car, cart-pole balancing, and cart-pole swing-up. Our experimental results demonstrate high-performing, interpretable fuzzy policies.

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning using point process theory. Likelihood functions for point pattern data derived from point process theory enable principled yet conceptually transparent extensions of learning tasks, such as classification, novelty detection and clustering, to point pattern data. Furthermore, tractable point pattern models as well as solutions for learning and decision making from point pattern data are developed.

In actuality, there exists much fuzzy knowledge which is uncertain or probabilistic of its nature. Especially human thinking is more associated with the fuzzy information. Humans can give acceptable answers, which are probably correct whereas our system at times lacks the similar ability as they are based upon classical set theory and two valued logic which only accepts "True" or "False". To enable our systems to give complete information rather than just accepting the value of 0 and 1 and give opinions. Fuzzy sets have been able to give solutions to many real world problems.

So, it is very important to predict the loan type and loan amount based on the banks' data. In this blog post, we will discuss about how Naive Bayes Classification model using R can be used to predict the loans. As there are more than two independent variables in customer data, it is difficult to plot chart as two dimensions are needed to better visualize how Machine Learning models work. In this blog post, Naive Bayes Classification Model with R is used.

In practice, proper tuning of t-SNE perplexity requires users to understand the inner working of the method as well as to have hands-on experience. We propose a model selection objective for t-SNE perplexity that requires negligible extra computation beyond that of the t-SNE itself. We empirically validate that the perplexity settings found by our approach are consistent with preferences elicited from human experts across a number of datasets. The similarities of our approach to Bayesian information criteria (BIC) and minimum description length (MDL) are also analyzed.

In recent years, the search for numerical algorithms which return probability distributions over the solution for a given numerical problem has become an active area of research [25]. Several models and methods have been proposed for the solution of initial value problems (IVPs) [57, 7, 51, 9, 31, 61]. However, these probabilistic algorithms have no immediate connection to the extensive literature on this task in numerical analysis. Most importantly, such inference algorithms do not come with convergence analysis out of the box. The methods in [7, 9, 61] have convergence results, but their respective implementations are based on sampling schemes and, thus, do not offer guarantees for individual runs. The methods in [51, 31] offer a deterministic execution and an analytical guarantee for the first step, but we will show that this guarantee is lacking for the whole integration domain. In this paper, we present a class of probabilistic solvers which combine properties of the standard and the probabilistic algorithms. We formulate desiderata that users might have for a probabilistic numerical algorithm.