Finite mixture models have been used for unsupervised learning for some time, and their use within the semi-supervised paradigm is becoming more commonplace. Clickstream data is one of the various emerging data types that demands particular attention because there is a notable paucity of statistical learning approaches currently available. A mixture of first-order continuous time Markov models is introduced for unsupervised and semi-supervised learning of clickstream data. This approach assumes continuous time, which distinguishes it from existing mixture model-based approaches; practically, this allows account to be taken of the amount of time each user spends on each webpage. The approach is evaluated, and compared to the discrete time approach, using simulated and real data.

Slot-filling refers to the task of annotating individual terms in a query with the corresponding intended product characteristics (product type, brand, gender, size, color, etc.). These characteristics can then be used by a search engine to return results that better match the query's product intent. Traditional methods for slot-filling require the availability of training data with ground truth slot-annotation information. However, generating such labeled data, especially in e-commerce is expensive and time-consuming because the number of slots increases as new products are added. In this paper, we present distant-supervised probabilistic generative models, that require no manual annotation. The proposed approaches leverage the readily available historical query logs and the purchases that these queries led to, and also exploit co-occurrence information among the slots in order to identify intended product characteristics. We evaluate our approaches by considering how they affect retrieval performance, as well as how well they classify the slots. In terms of retrieval, our approaches achieve better ranking performance (up to 156%) over Okapi BM25. Moreover, our approach that leverages co-occurrence information leads to better performance than the one that does not on both the retrieval and slot classification tasks.

We study reinforcement learning (RL) with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model (Jia et al., 2020; Ayoub et al., 2020; Zhou et al., 2020) and the learning agent has access to either an integration or a sampling oracle of the individual basis kernels. We propose a new Bernstein-type concentration inequality for self-normalized martingales for linear bandit problems with bounded noise. Based on the new inequality, we propose a new, computationally efficient algorithm with linear function approximation named $\text{UCRL-VTR}^{+}$ for the aforementioned linear mixture MDPs in the episodic undiscounted setting. We show that $\text{UCRL-VTR}^{+}$ attains an $\tilde O(dH\sqrt{T})$ regret where $d$ is the dimension of feature mapping, $H$ is the length of the episode and $T$ is the number of interactions with the MDP. We also prove a matching lower bound $\Omega(dH\sqrt{T})$ for this setting, which shows that $\text{UCRL-VTR}^{+}$ is minimax optimal up to logarithmic factors. In addition, we propose the $\text{UCLK}^{+}$ algorithm for the same family of MDPs under discounting and show that it attains an $\tilde O(d\sqrt{T}/(1-\gamma)^{1.5})$ regret, where $\gamma\in [0,1)$ is the discount factor. Our upper bound matches the lower bound $\Omega(d\sqrt{T}/(1-\gamma)^{1.5})$ proved in Zhou et al. (2020) up to logarithmic factors, suggesting that $\text{UCLK}^{+}$ is nearly minimax optimal. To the best of our knowledge, these are the first computationally efficient, nearly minimax optimal algorithms for RL with linear function approximation.

We present a machine learning framework and a new test bed for data mining from the Slurm Workload Manager for high-performance computing (HPC) clusters. The focus was to find a method for selecting features to support decisions: helping users decide whether to resubmit failed jobs with boosted CPU and memory allocations or migrate them to a computing cloud. This task was cast as both supervised classification and regression learning, specifically, sequential problem solving suitable for reinforcement learning. Selecting relevant features can improve training accuracy, reduce training time, and produce a more comprehensible model, with an intelligent system that can explain predictions and inferences. We present a supervised learning model trained on a Simple Linux Utility for Resource Management (Slurm) data set of HPC jobs using three different techniques for selecting features: linear regression, lasso, and ridge regression. Our data set represented both HPC jobs that failed and those that succeeded, so our model was reliable, less likely to overfit, and generalizable. Our model achieved an R^2 of 95\% with 99\% accuracy. We identified five predictors for both CPU and memory properties.

Service robots need to reason to support people in daily life situations. Reasoning is an expensive resource that should be used on demand whenever the expectations of the robot do not match the situation of the world and the execution of the task is broken down; in such scenarios the robot must perform the common sense daily life inference cycle consisting on diagnosing what happened, deciding what to do about it, and inducing and executing a plan, recurring in such behavior until the service task can be resumed. Here we examine two strategies to implement this cycle: (1) a pipe-line strategy involving abduction, decision-making and planning, which we call deliberative inference and (2) the use of the knowledge and preferences stored in the robot's knowledge-base, which we call conceptual inference. The former involves an explicit definition of a problem space that is explored through heuristic search, and the latter is based on conceptual knowledge including the human user preferences, and its representation requires a non-monotonic knowledge-based system. We compare the strengths and limitations of both approaches. We also describe a service robot conceptual model and architecture capable of supporting the daily life inference cycle during the execution of a robotics service task. The model is centered in the declarative specification and interpretation of robot's communication and task structure. We also show the implementation of this framework in the fully autonomous robot Golem-III. The framework is illustrated with two demonstration scenarios.

Recurrent Neural Networks (RNNs) have achieved remarkable performance on a range of tasks. A key step to further empowering RNN-based approaches is improving their explainability and interpretability. In this work we present MEME: a model extraction approach capable of approximating RNNs with interpretable models represented by human-understandable concepts and their interactions. We demonstrate how MEME can be applied to two multivariate, continuous data case studies: Room Occupation Prediction, and In-Hospital Mortality Prediction. Using these case-studies, we show how our extracted models can be used to interpret RNNs both locally and globally, by approximating RNN decision-making via interpretable concept interactions.

Contrastive divergence (CD) learning is a classical method for fitting unnormalized statistical models to data samples. Despite its wide-spread use, the convergence properties of this algorithm are still not well understood. The main source of difficulty is an unjustified approximation which has been used to derive the gradient of the loss. In this paper, we present an alternative derivation of CD that does not require any approximation and sheds new light on the objective that is actually being optimized by the algorithm. Specifically, we show that CD is an adversarial learning procedure, where a discriminator attempts to classify whether a Markov chain generated from the model has been time-reversed. Thus, although predating generative adversarial networks (GANs) by more than a decade, CD is, in fact, closely related to these techniques. Our derivation settles well with previous observations, which have concluded that CD's update steps cannot be expressed as the gradients of any fixed objective function. In addition, as a byproduct, our derivation reveals a simple correction that can be used as an alternative to Metropolis-Hastings rejection, which is required when the underlying Markov chain is inexact (e.g. when using Langevin dynamics with a large step).

The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for planning in UMDPs to find robust policies which are not overly conservative. In this work, we focus on planning for Stochastic Shortest Path (SSP) UMDPs with uncertain cost and transition functions. We introduce a Bellman equation to compute the regret for a policy. We propose a dynamic programming algorithm that utilises the regret Bellman equation, and show that it optimises minimax regret exactly for UMDPs with independent uncertainties. For coupled uncertainties, we extend our approach to use options to enable a trade off between computation and solution quality. We evaluate our approach on both synthetic and real-world domains, showing that it significantly outperforms existing baselines.

First and foremost, it is a delicious fruit. But there is a double delight for fruit-lover data scientists! It is also a Python package that implements fast and flexible probabilistic models ranging from individual probability distributions to compositional models such as Bayesian networks and Hidden Markov Models. The central idea behind this package is that all probabilistic models can be viewed as a probability distribution. That means they all yield probability estimates for samples and can be updated/fitted given samples and their associated weights.

We present a model for Bayesian filtering (BF) in discrete dynamic systems where multiple entities (inter)-act, i.e. where the system dynamics is naturally described by a Multiset rewriting system (MRS). Typically, BF in such situations is computationally expensive due to the high number of discrete states that need to be maintained explicitly. We devise a lifted state representation, based on a suitable decomposition of multiset states, such that some factors of the distribution are exchangeable and thus afford an efficient representation. Intuitively, this representation groups together similar entities whose properties follow an exchangeable joint distribution. Subsequently, we introduce a BF algorithm that works directly on lifted states, without resorting to the original, much larger ground representation. This algorithm directly lends itself to approximate versions by limiting the number of explicitly represented lifted states in the posterior. We show empirically that the lifted representation can lead to a factorial reduction in the representational complexity of the distribution, and in the approximate cases can lead to a lower variance of the estimate and a lower estimation error compared to the original, ground representation.