In many real applications, the input data are naturally expressed as tensors, such as virtual metrology in semiconductor manufacturing, face recognition and gait recognition in computer vision, etc. In this paper, we propose a general optimization framework for dealing with tensor inputs. Most existing methods for supervised tensor learning use only rank-one weight tensors in the linear model and cannot readily incorporate domain knowledge. In our framework, we obtain the weight tensor in a hierarchical way — we first approximate it by a low-rank tensor, and then estimate the low-rank approximation using the prior knowledge from various sources, e.g., different domain experts. This is motivated by wafer quality prediction in semiconductor manufacturing. Furthermore, we propose an effective algorithm named H-MOTE for solving this framework, which is guaranteed to converge. The time complexity of H-MOTE is linear with respect to the number of examples as well as the size of the weight tensor. Experimental results show the superiority of H-MOTE over state-of-the-art techniques on both synthetic and real data sets.

The recent popularization of social web services has made them one of the primary uses of the World Wide Web. An important concept in social web services is social actions such as making connections and communicating with others and adding annotations to web resources. Predicting social actions would improve many fundamental web applications, such as recommendations and web searches. One remarkable characteristic of social actions is that they involve multiple and heterogeneous objects such as users, documents, keywords, and locations. However, the high-dimensional property of such multinomial relations poses one fundamental challenge, that is, predicting multinomial relations with only a limited amount of data. In this paper, we propose a new multinomial relation prediction method, which is robust to data sparsity. We transform each instance of a multinomial relation into a set of binomial relations between the objects and the multinomial relation of the involved objects. We then apply an extension of a low-dimensional embedding technique to these binomial relations, which results in a generalized eigenvalue problem guaranteeing global optimal solutions. We also incorporate attribute information as side information to address the “cold start” problem in multinomial relation prediction. Experiments with various real-world social web service datasets demonstrate that the proposed method is more robust against data sparseness as compared to several existing methods, which can only find sub-optimal solutions.

We study time-consistency of optimization problems, where we say that an optimization problem is time-consistent if its optimal solution, or the optimal policy for choosing actions, does not depend on when the optimization problem is solved. Time-consistency is a minimal requirement on an optimization problem for the decisions made based on its solution to be rational. We show that the return that we can gain by taking "optimal" actions selected by solving a time-inconsistent optimization problem can be surely dominated by that we could gain by taking "suboptimal" actions. We establish sufficient conditions on the objective function and on the constraints for an optimization problem to be time-consistent. We also show when the sufficient conditions are necessary. Our results are relevant in stochastic settings particularly when the objective function is a risk measure other than expectation or when there is a constraint on a risk measure.

The trust region step problem, by solving a sphere constrained quadratic programming, plays a critical role in the trust region Newton method. In this paper, we propose an efficient Multi-Stage Conjugate Gradient (MSCG) algorithm to compute the trust region step in a multi-stage manner. Specifically, when the iterative solution is in the interior of the sphere, we perform the conjugate gradient procedure. Otherwise, we perform a gradient descent procedure which points to the inner of the sphere and can make the next iterative solution be a interior point. Subsequently, we proceed with the conjugate gradient procedure again. We repeat the above procedures until convergence. We also present a theoretical analysis which shows that the MSCG algorithm converges. Moreover, the proposed MSCG algorithm can generate a solution in any prescribed precision controlled by a tolerance parameter which is the only parameter we need. Experimental results on large-scale text data sets demonstrate our proposed MSCG algorithm has a faster convergence speed compared with the state-of-the-art algorithms.

We address the problem of spatial conservation planning in which the goal is to maximize the expected spread of cascades of an endangered species by strategically purchasing land parcels within a given budget. This problem can be solved by standard integer programming methods using the sample average approximation (SAA) scheme. Our main contribution lies in exploiting the separable structure present in this problem and using Lagrangian relaxation techniques to gain scalability over the flat representation. We also generalize the approach to allow the application of the SAA scheme to a range of stochastic optimization problems. Our iterative approach is highly efficient in terms of space requirements and it provides an upper bound over the optimal solution at each iteration. We apply our approach to the Red-cockaded Woodpecker conservation problem. The results show that it can find the optimal solution significantly faster---sometimes by an order-of-magnitude---than using the flat representation for a range of budget sizes.

Recently, graph-based ranking algorithms have received considerable interests in machine learning, computer vision and information retrieval communities. Ranking on data manifold (or manifold ranking, MR) is one of the representative approaches. One of the limitations of manifold ranking is its high computational complexity (O( n 3 ), where n is the number of samples in database). In this paper, we cast the manifold ranking into a Bregman divergence optimization framework under which we transform the original MR to an equivalent optimal kernel matrix learning problem.With this new formulation, two effective and efficient extensions are proposed to enhance the ranking performance. Extensive experimental results on two real world image databases show the effectiveness of the proposed approach.

One of the most challenging problems on modern urban planning and one of the goals to be solved for smart city design is that of urban waste disposal. Given urban population growth, and that the amount of waste generated by each of us citizens is also growing, the total amount of waste to be collected and treated is growing dramatically (EPA 2011), becoming one sensitive issue for local governments. A modern technique for waste collection that is steadily being adopted is automated vacuum waste collection. This technology uses air suction on a closed network of underground pipes to move waste from the collection points to the processing station, reducing greenhouse gas emissions as well as inconveniences to citizens (odors, noise, . . . ) and allowing better waste reuse and recycling. This technique is open to optimize energy consumption because moving huge amounts of waste by air impulsion requires a lot of electric power. The described problem challenge here is, precisely, that of organizing and scheduling waste collection to minimize the amount of energy per ton of collected waste in such a system via the use of Artificial Intelligence techniques. This kind of problems are an inviting opportunity to showcase the possibilities that AI for Computational Sustainability offers.

As an emerging machine learning and information retrieval technique, the matrix completion has been successfully applied to solve many scientific applications, such as collaborative prediction in information retrieval, video completion in computer vision, \emph{etc}. The matrix completion is to recover a low-rank matrix with a fraction of its entries arbitrarily corrupted. Instead of solving the popularly used trace norm or nuclear norm based objective, we directly minimize the original formulations of trace norm and rank norm. We propose a novel Schatten $p$-Norm optimization framework that unifies different norm formulations. An efficient algorithm is derived to solve the new objective and followed by the rigorous theoretical proof on the convergence. The previous main solution strategy for this problem requires computing singular value decompositions - a task that requires increasingly cost as matrix sizes and rank increase. Our algorithm has closed form solution in each iteration, hence it converges fast. As a consequence, our algorithm has the capacity of solving large-scale matrix completion problems. Empirical studies on the recommendation system data sets demonstrate the promising performance of our new optimization framework and efficient algorithm.

Kernelized sorting is a method for aligning objects across two domains by considering within-domain similarity, without a need to specify a cross-domain similarity measure. In this paper we present the Convex Kernelized Sorting method where, unlike in the previous approaches, the cross-domain object matching is formulated as a convex optimization problem, leading to simpler optimization and global optimum solution. Our method outputs soft alignments between objects, which can be used to rank the best matches for each object, or to visualize the object matching and verify the correct choice of the kernel. It also allows for computing hard one-to-one alignments by solving the resulting Linear Assignment Problem. Experiments on a number of cross-domain matching tasks show the strength of the proposed method, which consistently achieves higher accuracy than the existing methods.

This paper presents the design and learning architecture for an omnidirectional walk used by a humanoid robot soccer agent acting in the RoboCup 3D simulation environment. The walk, which was originally designed for and tested on an actual Nao robot before being employed in the 2011 RoboCup 3D simulation competition, was the crucial component in the UT Austin Villa team winning the competition in 2011. To the best of our knowledge, this is the first time that robot behavior has been conceived and constructed on a real robot for the end purpose of being used in simulation.  The walk is based on a double linear inverted pendulum model, and multiple sets of its parameters are optimized via a novel framework. The framework optimizes parameters for different tasks in conjunction with one another, a little-understood problem with substantial practical significance.  Detailed experiments show that the UT Austin Villa agent significantly outperforms all the other agents in the competition with the optimized walk being the key to its success.