Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one of the mechanisms behind these biological oscillations. However, while identifying cyclically expressed genes from time series measurements is relatively easy, determining the structure of the interaction network underpinning the oscillation is a far more challenging problem. Here, we explicitly leverage the oscillatory nature of the transcriptional signals and present a method for reconstructing network interactions tailored to this special but important class of genetic circuits. Our method is based on projecting the signal onto a set of oscillatory basis functions using a Discrete Fourier Transform. We build a Bayesian Hierarchical model within a frequency domain linear model in order to enforce sparsity and incorporate prior knowledge about the network structure. Experiments on real and simulated data show that the method can lead to substantial improvements over competing approaches if the oscillatory assumption is met, and remains competitive also in cases it is not.

Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by drawing parallels between Lacanian theory and Bayesian probability theory, and concludes that the latter must be enriched with causal interventions to model agency. The central contribution of this work is an abstract model of the subject that accommodates causal interventions in a measure-theoretic formalisation. This formalisation is obtained through a game-theoretic Ansatz based on modelling the inside and outside of the subject as an extensive-form game with imperfect information between two players. Finally, I illustrate the expressiveness of this model with an example of causal induction.

In this paper we present a `stability theorem' for stochastic approximation (SA) algorithms with `controlled Markov' noise. Such algorithms were first studied by Borkar in 2006. Specifically, sufficient conditions are presented which guarantee the stability of the iterates. Further, under these conditions the iterates are shown to track a solution to the differential inclusion defined in terms of the ergodic occupation measures associated with the `controlled Markov' process. As an application to our main result we present an improvement to a general form of temporal difference learning algorithms. Specifically, we present sufficient conditions for their stability and convergence using our framework. This paper builds on the works of Borkar as well as Benveniste, Metivier and Priouret.

Within the natural language processing (NLP) community, active learning has been widely investigated and applied in order to alleviate the annotation bottleneck faced by developers of new NLP systems and technologies. This paper presents the first theoretical analysis of stopping active learning based on stabilizing predictions (SP). The analysis has revealed three elements that are central to the success of the SP method: (1) bounds on Cohen's Kappa agreement between successively trained models impose bounds on differences in F-measure performance of the models; (2) since the stop set does not have to be labeled, it can be made large in practice, helping to guarantee that the results transfer to previously unseen streams of examples at test/application time; and (3) good (low variance) sample estimates of Kappa between successive models can be obtained. Proofs of relationships between the level of Kappa agreement and the difference in performance between consecutive models are presented. Specifically, if the Kappa agreement between two models exceeds a threshold T (where $T>0$), then the difference in F-measure performance between those models is bounded above by $\frac{4(1-T)}{T}$ in all cases. If precision of the positive conjunction of the models is assumed to be $p$, then the bound can be tightened to $\frac{4(1-T)}{(p+1)T}$.

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In the present paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an \textsf{spd} constraint may perform as well as regularization-based approaches with a proper choice of the regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squares estimation comes without any tuning parameter and may hence be preferred due to its simplicity.

We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Motivated by the studies that show many normal physiological systems involve irregularity while the decrease of irregularity usually implies the abnormality, the statistics for "outliers" in the components are used as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.

Definition of an accurate system model for Automated Planner (AP) is often impractical, especially for real-world problems. Conversely, off-the-shelf planners fail to scale up and are domain dependent. These drawbacks are inherited from conventional transition systems such as Finite State Machines (FSMs) that describes the action-plan execution generated by the AP. On the other hand, Behavior Trees (BTs) represent a valid alternative to FSMs presenting many advantages in terms of modularity, reactiveness, scalability and domain-independence. In this paper, we propose a model-free AP framework using Genetic Programming (GP) to derive an optimal BT for an autonomous agent to achieve a given goal in unknown (but fully observable) environments. We illustrate the proposed framework using experiments conducted with an open source benchmark Mario AI for automated generation of BTs that can play the game character Mario to complete a certain level at various levels of difficulty to include enemies and obstacles.

We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover the true graph. The resulting algorithm only requires a pairwise distance matrix as input and is computationally even more efficient than calculating the minimum spanning tree. We consider graph estimation problems under different settings, including discrete and nonparametric distribution families. Thorough numerical results are provided to illustrate the usefulness of the proposed method.

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussian quadrature based methods with suitably selected covariance functions. We show that this interpretation also extends to more general multivariate Gauss--Hermite integration methods and related spherical cubature rules. Additionally, we discuss different criteria for selecting the sigma-point locations: exactness for multivariate polynomials up to a given order, minimum average error, and quasi-random point sets. The performance of the different methods is tested in numerical experiments.

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inner product between the images of two data points in the feature space. Central to any kernel method is the kernel matrix, which is built by evaluating the kernel function on a given sample dataset. In this paper, we initiate the study of non-asymptotic spectral theory of random kernel matrices. These are n x n random matrices whose (i,j)th entry is obtained by evaluating the kernel function on $x_i$ and $x_j$, where $x_1,...,x_n$ are a set of n independent random high-dimensional vectors. Our main contribution is to obtain tight upper bounds on the spectral norm (largest eigenvalue) of random kernel matrices constructed by commonly used kernel functions based on polynomials and Gaussian radial basis. As an application of these results, we provide lower bounds on the distortion needed for releasing the coefficients of kernel ridge regression under attribute privacy, a general privacy notion which captures a large class of privacy definitions. Kernel ridge regression is standard method for performing non-parametric regression that regularly outperforms traditional regression approaches in various domains. Our privacy distortion lower bounds are the first for any kernel technique, and our analysis assumes realistic scenarios for the input, unlike all previous lower bounds for other release problems which only hold under very restrictive input settings.