A fundamental task that spans numerous applications is inference and uncertainty quantification for linear functionals of the eigenvectors of an unknown low-rank matrix. We prove that this task can be accomplished in a setting where the true matrix is symmetric and the additive noise matrix contains independent (and non-symmetric) entries. Specifically, we develop algorithms that produce confidence intervals for linear forms of individual eigenvectors, based on eigen-decomposition of the asymmetric data matrix followed by a careful de-biasing scheme. The proposed procedures and the accompanying theory enjoy several important features: (1) distribution-free (i.e. prior knowledge about the noise distributions is not needed); (2) adaptive to heteroscedastic noise; (3) statistically optimal under Gaussian noise. Along the way, we establish procedures to construct optimal confidence intervals for the eigenvalues of interest. All this happens under minimal eigenvalue separation, a condition that goes far beyond what generic matrix perturbation theory has to offer. Our studies fall under the category of "fine-grained" functional inference in low-complexity models.

An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit the number of these models that we can fit to neural data. Here we propose a unifying framework for modeling neural activity during decision-making tasks. The framework includes the canonical drift-diffusion model and enables extensions such as multi-dimensional accumulators, variable and collapsing boundaries, and discrete jumps. Our framework is based on constraining the parameters of recurrent state-space models, for which we introduce a scalable variational Laplace-EM inference algorithm. We applied the modeling approach to spiking responses recorded from monkey parietal cortex during two decision-making tasks. We found that a two-dimensional accumulator better captured the trial-averaged responses of a set of parietal neurons than a single accumulator model. Next, we identified a variable lower boundary in the responses of an LIP neuron during a random dot motion task.

A N -way array or N -th order tensor T is a multidimensional array in the product R I 1 ... I N of the vector spaces R I i for i 1, 2,...,N . A vector x R I 1 is a first-order tensor, and a matrix M R I 1 I 2 is a second-order tensor. The goal of NTF is to approximate a tensor T by a structured tensor X . Using the squared Frobenius norm as a distance metric, defined as nullXnull 2 F null j 1,j 2,...j NX 2 j 1j 2...j N, NTF is the following optimization problem: min a (i) p 0, 1 i N, 1 p r null null null null null nullT r null p 1 N null i 1a (i) p null null null null null null 2 F, (1) This work was supported by the Fonds de la Recherche Scientifique - FNRS and the Fonds Wetenschappelijk Onderzoek - Vlanderen (FWO) under EOS Project no O005318F-RG47, and by the European Research Council (ERC starting grant no 679515).

Tree ensemble methods such as random forests [Breiman, 2001] are very popular to handle high-dimensional tabular data sets, notably because of their good predictive accuracy. However, when machine learning is used for decision-making problems, settling for the best predictive procedures may not be reasonable since enlightened decisions require an in-depth comprehension of the algorithm prediction process. Unfortunately, random forests are not intrinsically interpretable since their prediction results from averaging several hundreds of decision trees. A classic approach to gain knowledge on this so-called black-box algorithm is to compute variable importances, that are employed to assess the predictive impact of each input variable. Variable importances are then used to rank or select variables and thus play a great role in data analysis. Nevertheless, there is no justification to use random forest variable importances in such way: we do not even know what these quantities estimate. In this paper, we analyze one of the two well-known random forest variable importances, the Mean Decrease Impurity (MDI). We prove that if input variables are independent and in absence of interactions, MDI provides a variance decomposition of the output, where the contribution of each variable is clearly identified. We also study models exhibiting dependence between input variables or interaction, for which the variable importance is intrinsically ill-defined. Our analysis shows that there may exist some benefits to use a forest compared to a single tree.

Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders, while some constraint-based methods can present them. This paper proposes a causal functional model-based method called repetitive causal discovery (RCD) to discover the causal structure of observed variables affected by latent confounders. RCD repeats inferring the causal directions between a small number of observed variables and determines whether the relationships are affected by latent confounders. RCD finally produces a causal graph where a bi-directed arrow indicates the pair of variables that have the same latent confounders, and a directed arrow indicates the causal direction of a pair of variables that are not affected by the same latent confounder. The results of experimental validation using simulated data and real-world data confirmed that RCD is effective in identifying latent confounders and causal directions between observed variables.

In the context of supervised statistical learning, it is typically assumed that the training set comes from the same distribution that draws the test samples. When this is not the case, the behavior of the learned model is unpredictable and becomes dependent upon the degree of similarity between the distribution of the training set and the distribution of the test set. One of the research topics that investigates this scenario is referred to as domain adaptation. Deep neural networks brought dramatic advances in pattern recognition and that is why there have been many attempts to provide good domain adaptation algorithms for these models. Here we take a different avenue and approach the problem from an incremental point of view, where the model is adapted to the new domain iteratively. We make use of an existing unsupervised domain-adaptation algorithm to identify the target samples on which there is greater confidence about their true label. The output of the model is analyzed in different ways to determine the candidate samples. The selected set is then added to the source training set by considering the labels provided by the network as ground truth, and the process is repeated until all target samples are labelled. Our results report a clear improvement with respect to the non-incremental case in several datasets, also outperforming other state-of-the-art domain adaptation algorithms.

Customers post online reviews at any time. With the timestamp of online reviews, they can be regarded as a flow of information. With this characteristic, designers can capture the changes in customer feedback to help set up product improvement strategies. Here we propose an approach for capturing changes of user expectation on product affordances based on the online reviews for two generations of products. First, the approach uses a rule-based natural language processing method to automatically identify and structure product affordances from review text. Then, inspired by the Kano model which classifies preferences of product attributes in five categories, conjoint analysis is used to quantitatively categorize the structured affordances. Finally, changes of user expectation can be found by applying the conjoint analysis on the online reviews posted for two successive generations of products. A case study based on the online reviews of Kindle e-readers downloaded from amazon.com shows that designers can use our proposed approach to evaluate their product improvement strategies for previous products and develop new product improvement strategies for future products.

Robots need models of human behavior for both inferring human goals and preferences, and predicting what people will do. A common model is the Boltzmann noisily-rational decision model, which assumes people approximately optimize a reward function and choose trajectories in proportion to their exponentiated reward. While this model has been successful in a variety of robotics domains, its roots lie in econometrics, and in modeling decisions among different discrete options, each with its own utility or reward. In contrast, human trajectories lie in a continuous space, with continuous-valued features that influence the reward function. We propose that it is time to rethink the Boltzmann model, and design it from the ground up to operate over such trajectory spaces. We introduce a model that explicitly accounts for distances between trajectories, rather than only their rewards. Rather than each trajectory affecting the decision independently, similar trajectories now affect the decision together. We start by showing that our model better explains human behavior in a user study. We then analyze the implications this has for robot inference, first in toy environments where we have ground truth and find more accurate inference, and finally for a 7DOF robot arm learning from user demonstrations.

We investigate some algorithmic properties of closed set and half-space separation in abstract closure systems. Assuming that the underlying closure system is finite and given by the corresponding closure operator, we show that the half-space separation problem is NP-complete. In contrast, for the relaxed problem of maximal closed set separation we give a greedy algorithm using linear number of queries (i.e., closure operator calls) and show that this bound is sharp. For a second direction to overcome the negative result above, we consider Kakutani closure systems and prove that they are algorithmically characterized by the greedy algorithm. As one of the major potential application fields, we then focus on Kakutani closure systems over graphs and generalize a fundamental characterization result based on the Pasch axiom to graph structured partitioning of finite sets. In addition, we give a sufficient condition for Kakutani closure systems over graphs in terms of graph minors. For a second application field, we consider closure systems over finite lattices, present an adaptation of the generic greedy algorithm to this kind of closure systems, and consider two potential applications. We show that for the special case of subset lattices over finite ground sets, e.g., for formal concept lattices, its query complexity is only logarithmic in the size of the lattice. The second application is concerned with finite subsumption lattices in inductive logic programming. We show that our method for separating two sets of first-order clauses from each other extends the traditional approach based on least general generalizations of first-order clauses. Though our primary focus is on the generality of the results obtained, we experimentally demonstrate the practical usefulness of the greedy algorithm on binary classification problems in Kakutani and non-Kakutani closure systems.

Relation Extraction (RE), the task of detecting and characterizing semantic relations between entities in text, has gained much importance in the last two decades, mainly in the biomedical domain. Many papers have been published on Relation Extraction using supervised machine learning techniques. Most of these techniques rely on statistical methods, such as feature-based and tree-kernels-based methods. Such statistical learning techniques are usually based on a propositional hypothesis space for representing examples, i.e., they employ an attribute-value representation of features. This kind of representation has some drawbacks, particularly in the extraction of complex relations which demand more contextual information about the involving instances, i.e., it is not able to effectively capture structural information from parse trees without loss of information. In this work, we present OntoILPER, a logic-based relational learning approach to Relation Extraction that uses Inductive Logic Programming for generating extraction models in the form of symbolic extraction rules. OntoILPER takes profit of a rich relational representation of examples, which can alleviate the aforementioned drawbacks. The proposed relational approach seems to be more suitable for Relation Extraction than statistical ones for several reasons that we argue. Moreover, OntoILPER uses a domain ontology that guides the background knowledge generation process and is used for storing the extracted relation instances. The induced extraction rules were evaluated on three protein-protein interaction datasets from the biomedical domain. The performance of OntoILPER extraction models was compared with other state-of-the-art RE systems. The encouraging results seem to demonstrate the effectiveness of the proposed solution.