We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count in the presence of an unweighted first-order model counting oracle. The algorithm has applications to inference in a variety of first-order probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, we make no assumptions on the form of the input sentence. Instead, our algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the first-order model counting oracle in practice using the approximate hashing-based model counter ApproxMC3, we show how our algorithm outperforms existing approximate and exact techniques for inference in first-order probabilistic models. We additionally provide PAC guarantees on the generated bounds.

The recent usage of technical systems in human-centric environments leads to the question, how to teach technical systems, e.g., robots, to understand, learn, and perform tasks desired by the human. Therefore, an accurate representation of knowledge is essential for the system to work as expected. This article mainly gives insight into different knowledge representation techniques and their categorization into various problem domains in artificial intelligence. Additionally, applications of presented knowledge representations are introduced in everyday robotics tasks. By means of the provided taxonomy, the search for a proper knowledge representation technique regarding a specific problem should be facilitated.

Let's face reality, mathematics is far from being enjoyable. To learn it, we often lack time, and most importantly, motivation. Why do we need all these symbols and a bunch of figures? It turns out, a lot of sense. Especially if you have something to do with machine learning. The point here is not to acquire knowledge, but to be able to use it.

This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances. We propose a new estimator, called MISC, that uses a mixed-integer optimization (MIO) program to find an optimal block diagonal structure specification for the covariance matrix, corresponding to subsets of correlated coefficients, for any desired sparsity level using Markov Chain Monte Carlo (MCMC) posterior draws from the unrestricted full covariance matrix. The optimal sparsity level of the covariance matrix is determined using out-of-sample validation. We demonstrate the ability of MISC to correctly recover the true covariance structure from synthetic data. In an empirical illustration using a stated preference survey on modes of transportation, we use MISC to obtain a sparse covariance matrix indicating how preferences for attributes are related to one another.

Variational Bayes is a method to find a good approximation of the posterior probability distribution of latent variables from a parametric family of distributions. The evidence lower bound (ELBO), which is nothing but the model evidence minus the Kullback-Leibler divergence, has been commonly used as a quality measure in the optimization process. However, the model evidence itself has been considered computationally intractable since it is expressed as a nested expectation with an outer expectation with respect to the training dataset and an inner conditional expectation with respect to latent variables. Similarly, if the Kullback-Leibler divergence is replaced with another divergence metric, the corresponding lower bound on the model evidence is often given by such a nested expectation. The standard (nested) Monte Carlo method can be used to estimate such quantities, whereas the resulting estimate is biased and the variance is often quite large. Recently the authors provided an unbiased estimator of the model evidence with small variance by applying the idea from multilevel Monte Carlo (MLMC) methods. In this article, we give more examples involving nested expectations in the context of variational Bayes where MLMC methods can help construct low-variance unbiased estimators, and provide numerical results which demonstrate the effectiveness of our proposed estimators.

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the Laplace distribution and Student-t distribution. However, the use of a non-Gaussian likelihood would incur the need for a computationally expensive Bayesian approximate computation in the posterior inferences. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function, and accordingly, the likelihood contains bias terms to explain the degree of deviations from the regression function. We entail how the biases can be estimated accurately with other hyperparameters by a regularized maximum likelihood estimation. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem with analytical forms of the predictive mean and variance estimates. Therefore, the proposed approach is simple and very computationally attractive. It also gives a very robust and accurate GP estimate for many tested scenarios. For the numerical evaluation, we perform a comprehensive simulation study to evaluate the proposed approach with the comparison to the existing robust GP approaches under various simulated scenarios of different outlier proportions and different noise levels. The approach is applied to data from two measurement systems, where the predictors are based on robust environmental parameter measurements and the response variables utilize more complex chemical sensing methods that contain a certain percentage of outliers. The utility of the measurement systems and value of the environmental data are improved through the computationally efficient GP regression and bias model.

With the rapid development of online education system, knowledge tracing which aims at predicting students' knowledge state is becoming a critical and fundamental task in personalized education. Traditionally, existing methods are domain-specified. However, there are a larger number of domains (e.g., subjects, schools) in the real world and the lacking of data in some domains, how to utilize the knowledge and information in other domains to help train a knowledge tracing model for target domains is increasingly important. We refer to this problem as domain adaptation for knowledge tracing (DAKT) which contains two aspects: (1) how to achieve great knowledge tracing performance in each domain. (2) how to transfer good performed knowledge tracing model between domains. To this end, in this paper, we propose a novel adaptable framework, namely adaptable knowledge tracing (AKT) to address the DAKT problem. Specifically, for the first aspect, we incorporate the educational characteristics (e.g., slip, guess, question texts) based on the deep knowledge tracing (DKT) to obtain a good performed knowledge tracing model. For the second aspect, we propose and adopt three domain adaptation processes. First, we pre-train an auto-encoder to select useful source instances for target model training. Second, we minimize the domain-specific knowledge state distribution discrepancy under maximum mean discrepancy (MMD) measurement to achieve domain adaptation. Third, we adopt fine-tuning to deal with the problem that the output dimension of source and target domain are different to make the model suitable for target domains. Extensive experimental results on two private datasets and seven public datasets clearly prove the effectiveness of AKT for great knowledge tracing performance and its superior transferable ability.

This letter proposes a novel reinforcement learning method for the synthesis of a control policy satisfying a control specification described by a linear temporal logic formula. We assume that the controlled system is modeled by a Markov decision process (MDP). We transform the specification to a limit-deterministic B\"uchi automaton (LDBA) with several accepting sets that accepts all infinite sequences satisfying the formula. The LDBA is augmented so that it explicitly records the previous visits to accepting sets. We take a product of the augmented LDBA and the MDP, based on which we define a reward function. The agent gets rewards whenever state transitions are in an accepting set that has not been visited for a certain number of steps. Consequently, sparsity of rewards is relaxed and optimal circulations among the accepting sets are learned. We show that the proposed method can learn an optimal policy when the discount factor is sufficiently close to one.

In order to collaborate safely and efficiently, robots need to anticipate how their human partners will behave. Some of today's robots model humans as if they were also robots, and assume users are always optimal. Other robots account for human limitations, and relax this assumption so that the human is noisily rational. Both of these models make sense when the human receives deterministic rewards: i.e., gaining either $100 or $130 with certainty. But in real world scenarios, rewards are rarely deterministic. Instead, we must make choices subject to risk and uncertainty--and in these settings, humans exhibit a cognitive bias towards suboptimal behavior. For example, when deciding between gaining $100 with certainty or $130 only 80% of the time, people tend to make the risk-averse choice--even though it leads to a lower expected gain! In this paper, we adopt a well-known Risk-Aware human model from behavioral economics called Cumulative Prospect Theory and enable robots to leverage this model during human-robot interaction (HRI). In our user studies, we offer supporting evidence that the Risk-Aware model more accurately predicts suboptimal human behavior. We find that this increased modeling accuracy results in safer and more efficient human-robot collaboration. Overall, we extend existing rational human models so that collaborative robots can anticipate and plan around suboptimal human behavior during HRI.

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.