As a well-known clustering algorithm, Fuzzy C-Means (FCM) allows each input sample to belong to more than one cluster, providing more flexibility than non-fuzzy clustering methods. However, the accuracy of FCM is subject to false detections caused by noisy records, weak feature selection and low certainty of the algorithm in some cases. The false detections are very important in some decision-making application domains like network security and medical diagnosis, where weak decisions based on such false detections may lead to catastrophic outcomes. They are mainly emerged from making decisions about a subset of records that do not provide enough evidence to make a good decision. In this paper, we propose a method for detecting such ambiguous records in FCM by introducing a certainty factor to decrease invalid detections. This approach enables us to send the detected ambiguous records to another discrimination method for a deeper investigation, thus increasing the accuracy by lowering the error rate. Most of the records are still processed quickly and with low error rate which prevents performance loss compared to similar hybrid methods. Experimental results of applying the proposed method on several datasets from different domains show a significant decrease in error rate as well as improved sensitivity of the algorithm.

A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the Neyman-Pearson sense. The algorithm is defined by a graph, at least one observation, and a diffusion model for threat. A link to well-known spectral detection methods is provided, and the equivalence of the random walk and harmonic solutions to the Bayesian formulation is proven. A general diffusion model is introduced that utilizes spatio-temporal relationships between vertices, and is used for a specific space-time formulation that leads to significant performance improvements on coordinated covert networks. This performance is demonstrated using a new hybrid mixed-membership blockmodel introduced to simulate random covert networks with realistic properties.

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximized over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximizing an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from iid observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the nonlinear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain inputs and semi-supervised Gaussian processes. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

In this work, we propose the marginal structured SVM (MSSVM) for structured prediction with hidden variables. MSSVM properly accounts for the uncertainty of hidden variables, and can significantly outperform the previously proposed latent structured SVM (LSSVM; Yu & Joachims (2009)) and other state-of-art methods, especially when that uncertainty is large. Our method also results in a smoother objective function, making gradient-based optimization of MSSVMs converge significantly faster than for LSSVMs. We also show that our method consistently outperforms hidden conditional random fields (HCRFs; Quattoni et al. (2007)) on both simulated and real-world datasets. Furthermore, we propose a unified framework that includes both our and several other existing methods as special cases, and provides insights into the comparison of different models in practice.

We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the application of a more flexible `spike-and-slab' distribution which models the absence or presence of a source's contribution independently of its strength if it contributes. We investigate two approaches to optimize the parameters of spike-and-slab sparse coding: a novel truncated EM approach and, for comparison, an approach based on standard factored variational distributions. The truncated approach can be regarded as a variational approach with truncated posteriors as variational distributions. In applications to source separation we find that both approaches improve the state-of-the-art in a number of standard benchmarks, which argues for the use of `spike-and-slab' priors for the corresponding data domains. Furthermore, we find that the truncated EM approach improves on the standard factored approach in source separation tasks$-$which hints to biases introduced by assuming posterior independence in the factored variational approach. Likewise, on a standard benchmark for image denoising, we find that the truncated EM approach improves on the factored variational approach. While the performance of the factored approach saturates with increasing numbers of hidden dimensions, the performance of the truncated approach improves the state-of-the-art for higher noise levels.

Recently, there has been a burst in the number of research projects on human computation via crowdsourcing. Multiple choice (or labeling) questions could be referred to as a common type of problem which is solved by this approach. As an application, crowd labeling is applied to find true labels for large machine learning datasets. Since crowds are not necessarily experts, the labels they provide are rather noisy and erroneous. This challenge is usually resolved by collecting multiple labels for each sample, and then aggregating them to estimate the true label. Although the mechanism leads to high-quality labels, it is not actually cost-effective. As a result, efforts are currently made to maximize the accuracy in estimating true labels, while fixing the number of acquired labels. This paper surveys methods to aggregate redundant crowd labels in order to estimate unknown true labels. It presents a unified statistical latent model where the differences among popular methods in the field correspond to different choices for the parameters of the model. Afterwards, algorithms to make inference on these models will be surveyed. Moreover, adaptive methods which iteratively collect labels based on the previously collected labels and estimated models will be discussed. In addition, this paper compares the distinguished methods, and provides guidelines for future work required to address the current open issues.

Map matching of GPS trajectories from a sequence of noisy observations serves the purpose of recovering the original routes in a road network. In this work in progress, we attempt to share our experience of feature construction in a spatial database by reporting our ongoing experiment of feature extrac-tion in Conditional Random Fields (CRFs) for map matching. Our preliminary results are obtained from real-world taxi GPS trajectories.

Map matching of the GPS trajectory serves the purpose of recovering the original route on a road network from a sequence of noisy GPS observations. It is a fundamental technique to many Location Based Services. However, map matching of a low sampling rate on urban road network is still a challenging task. In this paper, the characteristics of Conditional Random Fields with regard to inducing many contextual features and feature selection are explored for the map matching of the GPS trajectories at a low sampling rate. Experiments on a taxi trajectory dataset show that our method may achieve competitive results along with the success of reducing model complexity for computation-limited applications.

Neural Autoregressive Distribution Estimators (NADEs) have recently been shown as successful alternatives for modeling high dimensional multimodal distributions. One issue associated with NADEs is that they rely on a particular order of factorization for $P(\mathbf{x})$. This issue has been recently addressed by a variant of NADE called Orderless NADEs and its deeper version, Deep Orderless NADE. Orderless NADEs are trained based on a criterion that stochastically maximizes $P(\mathbf{x})$ with all possible orders of factorizations. Unfortunately, ancestral sampling from deep NADE is very expensive, corresponding to running through a neural net separately predicting each of the visible variables given some others. This work makes a connection between this criterion and the training criterion for Generative Stochastic Networks (GSNs). It shows that training NADEs in this way also trains a GSN, which defines a Markov chain associated with the NADE model. Based on this connection, we show an alternative way to sample from a trained Orderless NADE that allows to trade-off computing time and quality of the samples: a 3 to 10-fold speedup (taking into account the waste due to correlations between consecutive samples of the chain) can be obtained without noticeably reducing the quality of the samples. This is achieved using a novel sampling procedure for GSNs called annealed GSN sampling, similar to tempering methods that combines fast mixing (obtained thanks to steps at high noise levels) with accurate samples (obtained thanks to steps at low noise levels).

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of task relationships. In particular, we consider a joint estimation problem of the task relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship structure learning component builds on recent advances in structure learning of Gaussian graphical models based on sparse estimators of the precision (inverse covariance) matrix. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark datasets for regression and classification. We also consider the problem of combining climate model outputs for better projections of future climate, with focus on temperature in South America, and show that the proposed model outperforms several existing methods for the problem.