Video Friday is your weekly selection of awesome robotics videos, collected by your Automaton bloggers. We'll also be posting a weekly calendar of upcoming robotics events for the next few months; here's what we have so far (send us your events!): Let us know if you have suggestions for next week, and enjoy today's videos. The latest version of the self-solving Rubik's Cube is adorable in how it tries to throw itself off of the table it's solving itself on: Not exactly an optimised solve, but we'll forgive it, because that just means we get to watch it for longer. And here's what it looks like if you're holding it: When you think of robotics, you likely think of something rigid, heavy, and built for a specific purpose.

For those outside the fold, the Rubik's cube is cognitive kryptonite. Until this week, I'd certainly never solved one. Even now, saying that I solved a Rubik's cube feels like a grievous overstatement of my accomplishments. The truth is that we--a patient pre-teen "cuber" whose solve time is 47 seconds, her slightly-less-patient middle school teacher (whose solve time, she's embarrassed to admit, is closer to a minute and a half), and me--completed a cube together. The site of my public humiliation could not have been more incongruous with the task at hand.

Optimizing for local search is important, but if you aren't optimizing for mobile, you're going to miss out on your most important source of local traffic. For years, Google has been improving the relevance of local search, from its "Pigeon Update" to Promoted Pins. And since there are more searches on mobile than desktop, it's no wonder that Google has put a big emphasis on mobile-friendliness in its ranking algorithms. Taken together, that means that Google is putting a high priority on mobile local search -- and so should you. The fact of the matter is, more and more local searches are taking place on mobile.

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in polynomial time for suitable ranges of the parameter. In fact, random $K$-SAT, with $\alpha=M/N $ as control parameter, can be solved quickly for small enough values of $\alpha$. It shows a phase transition between a satisfiable phase and an unsatisfiable phase. For branch and bound algorithms, which operate in the space of feasible Boolean configurations, the empirically hardest problems are located only close to this phase transition. Here we study $K$-SAT ($K=3,4$) and the related optimization problem MAX-SAT by a linear programming approach, which is widely used for practical problems and allows for polynomial run time. In contrast to branch and bound it operates outside the space of feasible configurations. On the other hand, finding a solution within polynomial time is not guaranteed. We investigated several variants like including artificial objective functions, so called cutting-plane approaches, and a mapping to the NP-complete vertex-cover problem. We observed several easy-hard transitions, from where the problems are typically solvable (in polynomial time) using the given algorithms, respectively, to where they are not solvable in polynomial time. For the related vertex-cover problem on random graphs these easy-hard transitions can be identified with structural properties of the graphs, like percolation transitions. For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions. This renders the behaviour of random $K$-SAT more complex than, e.g., the vertex-cover problem.

The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We show that the problem is NP-hard, which justifies the usage of worst-case exponential-time as well as heuristic search methods. We then substantially improve the practical performance for both optimization styles by deriving a novel admissible bounding function that has an unbounded potential for additional pruning over the previously proposed one. Finally, we empirically investigate the approximation ratio of the greedy algorithm and show that it produces highly competitive results in a fraction of time needed for complete branch-and-bound style search.

Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear transformation with additive noise). ICA over finite fields is a special case of ICA in which both the observations and the independent components are over a finite alphabet. In this thesis we consider a formulation of the finite-field case in which an observation vector is decomposed to its independent components (as much as possible) with no prior assumption on the way it was generated. This generalization is also known as Barlow's minimal redundancy representation and is considered an open problem. We propose several theorems and show that this hard problem can be accurately solved with a branch and bound search tree algorithm, or tightly approximated with a series of linear problems. Moreover, we show that there exists a simple transformation (namely, order permutation) which provides a greedy yet very effective approximation of the optimal solution. We further show that while not every random vector can be efficiently decomposed into independent components, the vast majority of vectors do decompose very well (that is, within a small constant cost), as the dimension increases. In addition, we show that we may practically achieve this favorable constant cost with a complexity that is asymptotically linear in the alphabet size. Our contribution provides the first efficient set of solutions to Barlow's problem with theoretical and computational guarantees. Finally, we demonstrate our suggested framework in multiple source coding applications.

We compute the finite-sample minimax (modulo logarithmic factors) sample complexity of learning the parameters of a finite Markov chain from a single long sequence of states. Our error metric is a natural variant of total variation. The sample complexity necessarily depends on the spectral gap and minimal stationary probability of the unknown chain - for which, at least in the reversible case, there are known finite-sample estimators with fully empirical confidence intervals. To our knowledge, this is the first PAC-type result with nearly matching (up to logs) upper and lower bounds for learning, in any metric in the context of Markov chains.

The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures and under varying constraints. In this paper we focus on the exclusive row biclustering problem for gene expression data sets, in which each row can only be a member of a single bicluster while columns can participate in multiple ones. This type of biclustering may be adequate, for example, for clustering groups of cancer patients where each patient (row) is expected to be carrying only a single type of cancer, while each cancer type is associated with multiple (and possibly overlapping) genes (columns). We present a novel method to identify these exclusive row biclusters through a combination of existing biclustering algorithms and combinatorial auction techniques. We devise an approach for tuning the threshold for our algorithm based on comparison to a null model in the spirit of the Gap statistic approach [20]. We demonstrate our approach on both synthetic and real-world gene expression data and show its power in identifying large span non-overlapping rows sub matrices, while considering their unique nature. The Gap statistic approach succeeds in identifying appropriate thresholds in all our examples. This was presented at the IEEE International Conference in Data Mining at 2012 [22], and published at the Journal of Computer Science and Technology [23].

The design of neural network architectures is an important component for achieving state-of-the-art performance with machine learning systems across a broad array of tasks. Much work has endeavored to design and build architectures automatically through clever construction of a search space paired with simple learning algorithms. Recent progress has demonstrated that such meta-learning methods may exceed scalable human-invented architectures on image classification tasks. An open question is the degree to which such methods may generalize to new domains. In this work we explore the construction of meta-learning techniques for dense image prediction focused on the tasks of scene parsing, person-part segmentation, and semantic image segmentation. Constructing viable search spaces in this domain is challenging because of the multi-scale representation of visual information and the necessity to operate on high resolution imagery. Based on a survey of techniques in dense image prediction, we construct a recursive search space and demonstrate that even with efficient random search, we can identify architectures that outperform human-invented architectures and achieve state-of-the-art performance on three dense prediction tasks including 82.7\% on Cityscapes (street scene parsing), 71.3\% on PASCAL-Person-Part (person-part segmentation), and 87.9\% on PASCAL VOC 2012 (semantic image segmentation). Additionally, the resulting architecture is more computationally efficient, requiring half the parameters and half the computational cost as previous state of the art systems.

Dependability on AI models is of utmost importance to ensure full acceptance of the AI systems. One of the key aspects of the dependable AI system is to ensure that all its decisions are fair and not biased towards any individual. In this paper, we address the problem of detecting whether a model has an individual discrimination. Such a discrimination exists when two individuals who differ only in the values of their protected attributes (such as, gender/race) while the values of their non-protected ones are exactly the same, get different decisions. Measuring individual discrimination requires an exhaustive testing, which is infeasible for a non-trivial system. In this paper, we present an automated technique to generate test inputs, which is geared towards finding individual discrimination. Our technique combines the well-known technique called symbolic execution along with the local explainability for generation of effective test cases. Our experimental results clearly demonstrate that our technique produces 3.72 times more successful test cases than the existing state-of-the-art across all our chosen benchmarks.