Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.

Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability bounds for knowledge-seeking agents, and give a limit-computable weakly asymptotically optimal reinforcement learning agent.

Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean and covariance function, which determine the smoothness and variability of the function. The inference can then be conducted directly in the function space by evaluating or approximating the posterior process. Despite their attractive theoretical properties GPs provide practical challenges in their implementation. GPstuff is a versatile collection of computational tools for GP models compatible with Linux and Windows MATLAB and Octave. It includes, among others, various inference methods, sparse approximations and tools for model assessment. In this work, we review these tools and demonstrate the use of GPstuff in several models.

We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.