Computerized adaptive testing (CAT) is an interesting and promising approach to testing human abilities. In our research we use Bayesian networks to create a model of tested humans. We collected data from paper tests performed with grammar school students. In this article we first provide the summary of data used for our experiments. We propose several different Bayesian networks, which we tested and compared by cross-validation. Interesting results were obtained and are discussed in the paper. The analysis has brought a clearer view on the model selection problem. Future research is outlined in the concluding part of the paper.

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial analysis. Formally speaking, given a set of data instances, a clustering algorithm is expected to divide the set of data instances into the subsets which maximize the intra-subset similarity and inter-subset dissimilarity, where a similarity measure is defined beforehand. In this work, the state-of-the-arts clustering algorithms are reviewed from design concept to methodology; Different clustering paradigms are discussed. Advanced clustering algorithms are also discussed. After that, the existing clustering evaluation metrics are reviewed. A summary with future insights is provided at the end.

Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent variational methods for learning deep generative models, we introduce a unified algorithm to efficiently learn a broad spectrum of Kalman filters. Of particular interest is the use of temporal generative models for counterfactual inference. We investigate the efficacy of such models for counterfactual inference, and to that end we introduce the "Healing MNIST" dataset where long-term structure, noise and actions are applied to sequences of digits. We show the efficacy of our method for modeling this dataset. We further show how our model can be used for counterfactual inference for patients, based on electronic health record data of 8,000 patients over 4.5 years.

This paper considers the problem of cooperation between self-interested agents in acquiring better information regarding the nature of the different options and opportunities available to them. By sharing individual findings with others, the agents can potentially achieve a substantial improvement in overall and individual expected benefits. Unfortunately, it is well known that with self-interested agents equilibrium considerations often dictate solutions that are far from the fully cooperative ones, hence the agents do not manage to fully exploit the potential benefits encapsulated in such cooperation. In this paper we introduce, analyze and demonstrate the benefit of five methods aiming to improve cooperative information gathering. Common to all five that they constrain and limit the information sharing process. Nevertheless, the decrease in benefit due to the limited sharing is outweighed by the resulting substantial improvement in the equilibrium individual information gathering strategies. The equilibrium analysis given in the paper, which, in itself is an important contribution to the study of cooperation between self-interested agents, enables demonstrating that for a wide range of settings an improved individual expected benefit is achieved for all agents when applying each of the five methods.

What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a causal model for causal inference: given different experimental settings (for example various interventions) we collect all models that do show invariance in their predictive accuracy across settings and interventions. The causal model will be a member of this set of models with high probability. This approach yields valid confidence intervals for the causal relationships in quite general scenarios. We examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable. We further investigate robustness properties of our approach under model misspecification and discuss possible extensions. The empirical properties are studied for various data sets, including large-scale gene perturbation experiments.

This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.

Clustering is a common technique for statistical data analysis, widely used in data mining, machine learning, pattern recognition, image analysis, bioinformatics and cyber security. Conventional ("flat", "hard") clustering methods accept a finite metric space (O, d) as input and return a partition of O as their output. Hierarchical clustering (HC) methods have a different philosophy: their output is an entire hierarchy of partitions, called a dendrogram, capable of exhibiting multi-scale structure in the data set [1, 2]. Rather than fixing the required number of clusters in advance, as is common for many flat clustering algorithms, it is more informative to furnish a hierarchy of clusters, providing an opportunity to choose a partition at a scale most natural for the context of the task at hand. Many HC methods require linkage functions to provide a measure of dissimilarity between clusters (see [3, 4] for a fairly recent review). Some commonly used linkage functions are single linkage, complete linkage, average linkage, etc. The SLHC method, though suffering from the so called "chaining effect", remains popular for large scale applications [5] because of the low complexity of implementing it using minimum spanning trees (MST) [6].

As the name of the course suggests, this lecture note introduces readers to a neural network based approach to natural language understanding/processing. In order to make it as self-contained as possible, I spend much time on describing basics of machine learning and neural networks, only after which how they are used for natural languages is introduced. On the language front, I almost solely focus on language modelling and machine translation, two of which I personally find most fascinating and most fundamental to natural language understanding. After about a month of lectures and about 40 pages of writing this lecture note, I found this fascinating note [47] by Yoav Goldberg on neural network models for natural language processing. This note deals with wider topics on natural language processing with distributed representations in more details, and I highly recommend you to read it (hopefully along with this lecture note.)

Privacy preserving mechanisms such as differential privacy inject additional randomness in the form of noise in the data, beyond the sampling mechanism. Ignoring this additional noise can lead to inaccurate and invalid inferences. In this paper, we incorporate the privacy mechanism explicitly into the likelihood function by treating the original data as missing, with an end goal of estimating posterior distributions over model parameters. This leads to a principled way of performing valid statistical inference using private data, however, the corresponding likelihoods are intractable. In this paper, we derive fast and accurate variational approximations to tackle such intractable likelihoods that arise due to privacy. We focus on estimating posterior distributions of parameters of the naive Bayes log-linear model, where the sufficient statistics of this model are shared using a differentially private interface. Using a simulation study, we show that the posterior approximations outperform the naive method of ignoring the noise addition mechanism.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called \emph{decentralized stick-breaking policy representation} (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.