We introduce a semi-supervised discrete choice model to calibrate discrete choice models when relatively few requests have both choice sets and stated preferences but the majority only have the choice sets. Two classic semi-supervised learning algorithms, the expectation maximization algorithm and the cluster-and-label algorithm, have been adapted to our choice modeling problem setting. We also develop two new algorithms based on the cluster-and-label algorithm. The new algorithms use the Bayesian Information Criterion to evaluate a clustering setting to automatically adjust the number of clusters. Two computational studies including a hotel booking case and a large-scale airline itinerary shopping case are presented to evaluate the prediction accuracy and computational effort of the proposed algorithms. Algorithmic recommendations are rendered under various scenarios.

We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassification error, also provide sufficient conditions of sub-optimal classifiers and optimal classifiers. In implementation, a variational Bayes algorithm is developed to compute the posterior efficiently and could be parallelized to deal with the ultra-high dimensional case.

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals, where the sampling cost is a function of both the number of samples taken and the distance traveled during estimation. This is motivated by our work studying regions of low oxygen concentration in the Great Lakes. We show that for one-dimensional threshold classifiers, a tradeoff between the number of samples taken and distance traveled can be achieved using a generalization of binary search, which we refer to as quantile search. We characterize both the estimation error after a fixed number of samples and the distance traveled in the noiseless case, as well as the estimation error in the case of noisy measurements. We illustrate our results in both simulations and experiments and show that our method outperforms existing algorithms in the majority of practical scenarios.

In the last few months, I have had several people contact me about their enthusiasm for venturing into the world of data science and using Machine Learning (ML) techniques to probe statistical regularities and build impeccable data-driven products. However, I've observed that some actually lack the necessary mathematical intuition and framework to get useful results. This is the main reason I decided to write this blog post. Recently, there has been an upsurge in the availability of many easy-to-use machine and deep learning packages such as scikit-learn, Weka, Tensorflow etc. Machine Learning theory is a field that intersects statistical, probabilistic, computer science and algorithmic aspects arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. Despite the immense possibilities of Machine and Deep Learning, a thorough mathematical understanding of many of these techniques is necessary for a good grasp of the inner workings of the algorithms and getting good results.

Noname manuscript No. (will be inserted by the editor) Abstract Multi-label classification is a type of supervised learning where an instance may belong to multiple labels simultaneously. Predicting each label independently has been criticized for not exploiting any correlation between labels. In this paper we propose a novel approach, Nearest Labelset using Double Distances (NLDD), that predicts the labelset observed in the training data that minimizes a weighted sum of the distances in both the feature space and the label space to the new instance. The weights specify the relative tradeoff between the two distances. The weights are estimated from a binomial regression of the number of misclassified labels as a function of the two distances. Model parameters are estimated by maximum likelihood. NLDD only considers labelsets observed in the training data, thus implicitly taking into account label dependencies. Keywords Multi-label classification, Machine learning, Label correlations 1 Introduction In multi-label classification, an instance can belong to multiple labels at the same time. This is different from multi-class or binary classification, where an instance can only be associated with a single label.

The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose the use of a statistical shape model (SSM) as a prior for surface reconstruction. The SSM is represented by a point distribution model (PDM), which is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we formulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given points are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are "oriented" according to the surface normals at the PDM points, a surface-based fitting is accomplished. Estimating the parameters of the GMM in a maximum a posteriori manner yields the reconstruction of the surface from the given data points. We compare our method to the extensively used Iterative Closest Points method on several different anatomical datasets/SSMs (brain, femur, tibia, hip, liver) and demonstrate superior accuracy and robustness on sparse data.

Adverse drug reaction (ADR) is a major burden for patients and healthcare industry. It usually causes preventable hospitalizations and deaths, while associated with a huge amount of cost. Traditional preclinical in vitro safety profiling and clinical safety trials are restricted in terms of small scale, long duration, huge financial costs and limited statistical signifi- cance. The availability of large amounts of drug and ADR data potentially allows ADR predictions during the drugs’ early preclinical stage with data analytics methods to inform more targeted clinical safety tests. Despite their initial success, existing methods have trade-offs among interpretability, predictive power and efficiency. This urges us to explore methods that could have all these strengths and provide practical solutions for real world ADR predictions. We cast the ADR-drug relation structure into a three-layer hierarchical Bayesian model. We interpret each ADR as a symbolic word and apply latent Dirichlet allocation (LDA) to learn topics that may represent certain biochemical mechanism that relates ADRs with drug structures. Based on LDA, we designed an equivalent regularization term to incorporate the hierarchical ADR domain knowledge. Finally, we developed a mixed input model leveraging a fast collapsed Gibbs sampling method that the complexity of each iteration of Gibbs sampling proportional only to the number of positive ADRs. Experiments on real world data show our models achieved higher prediction accuracy and shorter running time than the state-of-the-art alternatives.

Structured knowledge about concepts plays an increasingly important role in areas such as information retrieval. The available ontologies and knowledge graphs that encode such conceptual knowledge, however, are inevitably incomplete. This observation has led to a number of methods that aim to automatically complete existing knowledge bases. Unfortunately, most existing approaches rely on black box models, e.g. formulated as global optimization problems, which makes it difficult to support the underlying reasoning process with intuitive explanations. In this paper, we propose a new method for knowledge base completion, which uses interpretable conceptual space representations and an explicit model for inductive inference that is closer to human forms of commonsense reasoning. Moreover, by separating the task of representation learning from inductive reasoning, our method is easier to apply in a wider variety of contexts. Finally, unlike optimization based approaches, our method can naturally be applied in settings where various logical constraints between the extensions of concepts need to be taken into account.

Spatial patterns embedded in human faces are crucial for differentiating posed expressions from spontaneous ones, yet they have not been thoroughly exploited in the literature. To tackle this problem, we present a generative model, i.e., Latent Regression Bayesian Network (LRBN), to effectively capture the spatial patterns embedded in facial landmark points to differentiate between posed and spontaneous facial expressions. The LRBN is a directed graphical model consisting of one latent layer and one visible layer. Due to the “explaining away“ effect in Bayesian networks, LRBN is able to capture both the dependencies among the latent variables given the observation and the dependencies among visible variables. We believe that such dependencies are crucial for faithful data representation. Specifically, during training, we construct two LRBNs to capture spatial patterns inherent in displacements of landmark points from spontaneous facial expressions and posed facial expressions respectively. During testing, the samples are classified into posed or spontaneous expressions according to their likelihoods on two models. Efficient learning and inference algorithms are proposed. Experimental results on two benchmark databases demonstrate the advantages of the proposed approach in modeling spatial patterns as well as its superior performance to the existing methods in differentiating between posed and spontaneous expressions.

The formalism of multi-objective influence diagrams has recently been developed for modeling and solving sequential decision problems under uncertainty and multiple objectives. Since utility values representing the decision maker's preferences are only partially ordered (e.g., by the Pareto order) we no longer have a unique maximal value of expected utility, but a set of them. Computing the set of maximal values of expected utility and the corresponding policies can be computationally very challenging. In this paper, we consider alternative notions of optimality, one of the most important one being the notion of possibly optimal, namely optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop a variable elimination algorithm for computing the set of possibly optimal expected utility values, prove formally its correctness, and compare variants of the algorithm experimentally.