We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a given text. Each inflected form is connected to its corresponding headword, which in some cases in non-unique. The resulting sparse graph decomposes into a large number of connected components, to be called word groups. We then show how the concept of the word group can be used to construct coverage curves of selected Latin texts. We also investigate a version of the inflection graph in which all theoretically possible inflected forms are included. Distribution of sizes of connected components of this graphs resembles cluster distribution in a lattice percolation near the critical point.

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization aspects.

We describe how to use propositional model counting for a quantitative analysis of product configuration data. Our approach computes valuable meta information such as the total number of valid configurations or the relative frequency of components. This information can be used to assess the severity of documentation errors or to measure documentation quality. As an application example we show how we apply these methods to product documentation formulas of the Mercedes-Benz line of vehicles. In order to process these large formulas we developed and implemented a new model counter for non-CNF formulas. Our model counter can process formulas, whose CNF representations could not be processed up till now.

Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that considers resource costs. Agents are formalized as probability measures over input-output streams. We postulate that any such probability measure can be assigned a corresponding conjugate utility function based on three axioms: utilities should be real-valued, additive and monotonic mappings of probabilities. We show that these axioms enforce a unique conversion law between utility and probability (and thereby, information). Moreover, we show that this relation can be characterized as a variational principle: given a utility function, its conjugate probability measure maximizes a free utility functional. Transformations of probability measures can then be formalized as a change in free utility due to the addition of new constraints expressed by a target utility function. Accordingly, one obtains a criterion to choose a probability measure that trades off the maximization of a target utility function and the cost of the deviation from a reference distribution. We show that optimal control, adaptive estimation and adaptive control problems can be solved this way in a resource-efficient way. When resource costs are ignored, the MEU principle is recovered. Our formalization might thus provide a principled approach to bounded rationality that establishes a close link to information theory.

The stable marriage (SM) problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. In the classical formulation, n men and n women express their preferences (via a strict total order) over the members of the other sex. Solving a SM problem means finding a stable marriage where stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. We consider both the classical stable marriage problem and one of its useful variations (denoted SMTI) where the men and women express their preferences in the form of an incomplete preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these lists, an we try to find a stable matching that marries as many people as possible. Whilst the SM problem is polynomial to solve, the SMTI problem is NP-hard. We propose to tackle both problems via a local search approach, which exploits properties of the problems to reduce the size of the neighborhood and to make local moves efficiently. We evaluate empirically our algorithm for SM problems by measuring its runtime behaviour and its ability to sample the lattice of all possible stable marriages. We evaluate our algorithm for SMTI problems in terms of both its runtime behaviour and its ability to find a maximum cardinality stable marriage.For SM problems, the number of steps of our algorithm grows only as O(nlog(n)), and that it samples very well the set of all stable marriages. It is thus a fair and efficient approach to generate stable marriages.Furthermore, our approach for SMTI problems is able to solve large problems, quickly returning stable matchings of large and often optimal size despite the NP-hardness of this problem.

Frequent Episode Discovery framework is a popular framework in Temporal Data Mining with many applications. Over the years many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper we present a unified view of all such frequency counting algorithms. We present a generic algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies and we present quantitative relationships among different frequencies. Our unified view also helps in obtaining correctness proofs for various algorithms as we show here. We also point out how this unified view helps us to consider generalization of the algorithm so that they can discover episodes with general partial orders.

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess risk of order d/n, where n is the size of the training data. Without this strong assumption, standard results often contain a multiplicative log n factor, and require some additional assumptions like uniform boundedness of the d-dimensional input representation and exponential moments of the output. This work provides new risk bounds for the ridge estimator and the ordinary least squares estimator, and their variants. It also provides shrinkage procedures with convergence rate d/n (i.e., without the logarithmic factor) in expectation and in deviations, under various assumptions. The key common surprising factor of these results is the absence of exponential moment condition on the output distribution while achieving exponential deviations. All risk bounds are obtained through a PAC-Bayesian analysis on truncated differences of losses. Finally, we show that some of these results are not particular to the least squares loss, but can be generalized to similar strongly convex loss functions.

Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has played an important role in both problem representation and reasoning. I describe recent work on using symmetry to help solve constraint satisfaction problems. Symmetries occur within individual solutions of problems as well as between different solutions of the same problem. Symmetry can also be applied to the constraints in a problem to give new symmetric constraints. Reasoning about symmetry can speed up problem solving, and has led to the discovery of new results in both graph and number theory.