It is no pure coincidence that an organic chemist rather than a computer specialist is writing this foreword.

Harold Shephard Samuel D. Thurman William T. Lake JOINDER OF CLAIMS, COUNTERCLAIMS, AND CROSS-COMPLAINTS: SUGGESTED REVISION OF THE CALIFORNIA PROVISIONS. Research in artificial intelligence, a branch of computer science, has illuminated our capacity to use computers to model human thought processes. In this Article we will argue that the time has come for serious interdisciplinary work between lawyers and computer scientists to explore the computer's potential in law. Interdisciplinary work between the lawyer and the computer scientist has floundered on the misconceptions that each has of the other's discipline. As a result, no one has yet attempted computer programs incorporating complex techniques of legal reasoning. Even efforts in legal information retrieval have been hampered by these misconceptions. In retrieval, lawyers have viewed the computer as, at most, a storehouse from which cases and statutes might be retrieved by skillfully designed indexing systems.

In this paper we discuss some reasons why temporal logic might not be suitable to model real life norms. To show this, we present a novel deontic logic contrary-to-duty/derived permission paradox based on the interaction of obligations, permissions and contrary-to-duty obligations. The paradox is inspired by real life norms.

This paper introduces and develops a novel variable importance score function in the context of ensemble learning and demonstrates its appeal both theoretically and empirically. Our proposed score function is simple and more straightforward than its counterpart proposed in the context of random forest, and by avoiding permutations, it is by design computationally more efficient than the random forest variable importance function. Just like the random forest variable importance function, our score handles both regression and classification seamlessly. One of the distinct advantage of our proposed score is the fact that it offers a natural cut off at zero, with all the positive scores indicating importance and significance, while the negative scores are deemed indications of insignificance. An extra advantage of our proposed score lies in the fact it works very well beyond ensemble of trees and can seamlessly be used with any base learners in the random subspace learning context. Our examples, both simulated and real, demonstrate that our proposed score does compete mostly favorably with the random forest score.

A number of representation schemes have been presented for use within learning classifier systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF learning classifier system. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous fuzzy logic networks in the continuous-valued case. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such dynamical systems within XCSF to solve a number of well-known test problems.

Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop prediction methods that perform well against complex benchmarks. In this paper, we address these two directions together. We present a fully adaptive method that competes with dynamic benchmarks in which regret guarantee scales with regularity of the sequence of cost functions and comparators. Notably, the regret bound adapts to the smaller complexity measure in the problem environment. Finally, we apply our results to drifting zero-sum, two-player games where both players achieve no regret guarantees against best sequences of actions in hindsight.

Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$ and $\mathcal{O}(n^2)$ respectively, and so is prohibitive in many cases. We propose approximations of KRR based on $m$-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension $m$ can be chosen while still preserving minimax optimality of the approximate KRR estimate. For various classes of randomized sketches, including those based on Gaussian and randomized Hadamard matrices, we prove that it suffices to choose the sketch dimension $m$ proportional to the statistical dimension (modulo logarithmic factors). Thus, we obtain fast and minimax optimal approximations to the KRR estimate for non-parametric regression.

We propose a topic modeling approach to the prediction of preferences in pairwise comparisons. We develop a new generative model for pairwise comparisons that accounts for multiple shared latent rankings that are prevalent in a population of users. This new model also captures inconsistent user behavior in a natural way. We show how the estimation of latent rankings in the new generative model can be formally reduced to the estimation of topics in a statistically equivalent topic modeling problem. We leverage recent advances in the topic modeling literature to develop an algorithm that can learn shared latent rankings with provable consistency as well as sample and computational complexity guarantees. We demonstrate that the new approach is empirically competitive with the current state-of-the-art approaches in predicting preferences on some semi-synthetic and real world datasets.

A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has previously been shown that when the kernel used in defining the joint embedding is characteristic (that is, the embedding of the joint distribution to the feature space is injective), then the HSIC-based test is consistent. In particular, it is sufficient for the product of kernels on the individual domains to be characteristic on the joint domain. In this note, it is established via a result of Lyons (2013) that HSIC-based independence tests are consistent when kernels on the marginals are characteristic on their respective domains, even when the product of kernels is not characteristic on the joint domain.

Distance weighted discrimination (DWD) was originally proposed to handle the data piling issue in the support vector machine. In this paper, we consider the sparse penalized DWD for high-dimensional classification. The state-of-the-art algorithm for solving the standard DWD is based on second-order cone programming, however such an algorithm does not work well for the sparse penalized DWD with high-dimensional data. In order to overcome the challenging computation difficulty, we develop a very efficient algorithm to compute the solution path of the sparse DWD at a given fine grid of regularization parameters. We implement the algorithm in a publicly available R package sdwd. We conduct extensive numerical experiments to demonstrate the computational efficiency and classification performance of our method.