We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended to a broader class of operators in the Gaussian case, via the Lo\`eve isometry. Several covariance-driven pathwise invariances are illustrated, including fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process regression.

Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many applications to ensure voltage stability and AC power flow feasibility. This paper proposes linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a convex approximation of the cosine terms in the AC equations, as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and MatPower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two "proof-of-concept" studies in power restoration and capacitor placement.

This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the present paper that, when including anisotropy detection to improve resolution on shock layer, SPH is a very peculiar case of unsupervised machine learning. On the other hand, the free particle nature of SPH opens an opportunity for artificial intelligence to study particles as agents acting in a collaborative framework in which the timed outcomes of a fluid simulation forms a large knowledge base, which might be very attractive in computational astrophysics phenomenological problems like self-propagating star formation.

The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift.

When solving extensive-form games with large action spaces, typically significant abstraction is needed to make the problem manageable from a modeling or computational perspective. When this occurs, a procedure is needed to interpret actions of the opponent that fall outside of our abstraction (by mapping them to actions in our abstraction). This is called an action translation mapping. Prior action translation mappings have been based on heuristics without theoretical justification. We show that the prior mappings are highly exploitable and that most of them violate certain natural desiderata. We present a new mapping that satisfies these desiderata and has significantly lower exploitability than the prior mappings. Furthermore, we observe that the cost of this worst-case performance benefit (low exploitability) is not high in practice; our mapping performs competitively with the prior mappings against no-limit Texas Hold'em agents submitted to the 2012 Annual Computer Poker Competition. We also observe several paradoxes that can arise when performing action abstraction and translation; for example, we show that it is possible to improve performance by including suboptimal actions in our abstraction and excluding optimal actions.

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression functions. The proposed estimation method is also efficient as its computation cost does not increase exponentially with the number of classes. The theoretical and numerical studies demonstrate that the proposed estimation method is highly competitive against the existing competitors, especially when the number of classes is relatively large.

The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of misclassifications differently when different classifiers are used. To overcome this, Hand (2009) proposed the $H$ measure, which allows a given researcher to fix the distribution of relative severities to a classifier-independent setting on a given problem. This note extends the discussion, and proposes a modified standard distribution for the $H$ measure, which better matches the requirements of researchers, in particular those faced with heavily unbalanced datasets, the $Beta(\pi_1+1,\pi_0+1)$ distribution. [Preprint submitted at Pattern Recognition Letters]

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. We demonstrate our fast simultaneous training of generalized linear models (FaSTGLZ) algorithm on a number of real-world datasets, and we run otherwise computationally intensive bootstrapping and permutation test analyses that are typically necessary for obtaining statistically rigorous classification results and meaningful interpretation. Code is freely available at http://liinc.bme.columbia.edu/fastglz.

A significant theoretical advantage of search-and-score methods for learning Bayesian Networks is that they can accept informative prior beliefs for each possible network, thus complementing the data. In this paper, a method is presented for assigning priors based on beliefs on the presence or absence of certain paths in the true network. Such beliefs correspond to knowledge about the possible causal and associative relations between pairs of variables. This type of knowledge naturally arises from prior experimental and observational data, among others. In addition, a novel search-operator is proposed to take advantage of such prior knowledge. Experiments show that, using path beliefs improves the learning of the skeleton, as well as the edge directions in the network.

The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis and clustering, especially for complex and high-dimensional data. Several R packages exist for level set tree estimation, but their practical usefulness is limited by computational inefficiency, absence of interactive graphical capabilities and, from a theoretical perspective, reliance on asymptotic approximations. To make it easier for practitioners to capture the advantages of level set trees, we have written the Python package DeBaCl for DEnsity-BAsed CLustering. In this article we illustrate how DeBaCl's level set tree estimates can be used for difficult clustering tasks and interactive graphical data analysis. The package is intended to promote the practical use of level set trees through improvements in computational efficiency and a high degree of user customization. In addition, the flexible algorithms implemented in DeBaCl enjoy finite sample accuracy, as demonstrated in recent literature on density clustering. Finally, we show the level set tree framework can be easily extended to deal with functional data.