The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work, we have considered the statistical problem of estimating the homology of a manifold from noiseless samples and from noisy samples under several different noise models. We derived upper and lower bounds on the minimax risk for this problem. In this note we revisit the noiseless case. In previous work we used Le Cam's lemma to establish a lower bound that differed from the upper bound of Niyogi, Smale and Weinberger by a polynomial factor in the condition number. In this note we use a different construction based on the direct analysis of the likelihood ratio test to show that the upper bound of Niyogi, Smale and Weinberger is in fact tight, thus establishing rate optimal asymptotic minimax bounds for the problem. The techniques we use here extend in a straightforward way to the noisy settings considered in our earlier work.

We present ReAct!, an interactive tool for high-level reasoning for cognitive robotic applications. ReAct! enables robotic researchers to describe robots' actions and change in dynamic domains, without having to know about the syntactic and semantic details of the underlying formalism in advance, and solve planning problems using state-of-the-art automated reasoners, without having to learn about their input/output language or usage. In particular, ReAct! can be used to represent sophisticated dynamic domains that feature concurrency, indirect effects of actions, and state/transition constraints. It allows for embedding externally defined calculations (e.g., checking for collision-free continuous trajectories) into representations of hybrid domains that require a tight integration of (discrete) high-level reasoning with (continuous) geometric reasoning. ReAct! also enables users to solve planning problems that involve complex goals. Such variety of utilities are useful for robotic researchers to work on interesting and challenging domains, ranging from service robotics to cognitive factories. ReAct! provides sample formalizations of some action domains (e.g., multi-agent path planning, Tower of Hanoi), as well as dynamic simulations of plans computed by a state-of-the-art automated reasoner (e.g., a SAT solver or an ASP solver).

We investigate different approaches to integrating object recognition and planning in a tabletop manipulation domain with the set of objects used in the 2012 RoboCup@Work competition. Results of our preliminary experiments show that, with some approaches, close integration of perception and planning improves the quality of plans, as well as the computation times of feasible plans.

We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually are violated. In this paper, we propose a new algorithm for learning causal orders that is robust against one typical violation of the model assumptions: latent confounders. The key idea is to detect latent confounders by testing independence between estimated external influences and find subsets (parcels) that include variables that are not affected by latent confounders. We demonstrate the effectiveness of our method using artificial data and simulated brain imaging data.

We study a simple modification to the conventional time of flight mass spectrometry (TOFMS) where a \emph{variable} and (pseudo)-\emph{random} pulsing rate is used which allows for traces from different pulses to overlap. This modification requires little alteration to the currently employed hardware. However, it requires a reconstruction method to recover the spectrum from highly aliased traces. We propose and demonstrate an efficient algorithm that can process massive TOFMS data using computational resources that can be considered modest with today's standards. This approach can be used to improve duty cycle, speed, and mass resolving power of TOFMS at the same time. We expect this to extend the applicability of TOFMS to new domains.

The combined approach of the Qualitative Reasoning and Probabilistic Functions for the knowledge representation is proposed. The method aims at represent uncertain, qualitative knowledge that is essential for the moving blocks task's execution. The attempt to formalize the commonsense knowledge is performed with the Situation Calculus language for reasoning and robot's beliefs representation. The method is implemented in the Prolog programming language and tested for a specific simulated scenario. In most cases the implementation enables us to solve a given task, i.e., move blocks to desired positions. The example of robot's reasoning and main parts of the implemented program's code are presented.

This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select changes that improve both the short-term and long-term performance of such systems. This work is illustrated by experiments carried out on the ad placement system associated with the Bing search engine.

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating the computationally cubic complexity of the multivariate Gaussian process. A Dirichlet process prior is adopted to allow the (possibly infinite) number of mixture components to be automatically inferred from training data, and Markov chain Monte Carlo sampling techniques are used for parameter and latent variable inference. Preliminary experimental results on multivariate regression show the feasibility of the proposed model.

We propose a new approach, multi-view Laplacian support vector machines (SVMs), for semi-supervised learning under the multi-view scenario. It integrates manifold regularization and multi-view regularization into the usual formulation of SVMs and is a natural extension of SVMs from supervised learning to multi-view semi-supervised learning. The function optimization problem in a reproducing kernel Hilbert space is converted to an optimization in a finite-dimensional Euclidean space. After providing a theoretical bound for the generalization performance of the proposed method, we further give a formulation of the empirical Rademacher complexity which affects the bound significantly. From this bound and the empirical Rademacher complexity, we can gain insights into the roles played by different regularization terms to the generalization performance. Experimental results on synthetic and real-world data sets are presented, which validate the effectiveness of the proposed multi-view Laplacian SVMs approach.

In the real world, robots with embodiment face various issues such as dynamic continuous changes of the environment and input/output disturbances. The key to solving these issues can be found in daily life; people `do actions associated with sensing' and `dynamically change their plans when necessary'. We propose the use of a new concept, enabling robots to do these two things, for autonomously controlling mobile robots. We implemented our concept to make two experiments under static/dynamic environments. The results of these experiments show that our idea provides a way to adapt to dynamic changes of the environment in the real world.