Parameter Estimation of Heavy-Tailed AR Model with Missing Data via Stochastic EM

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations is preferred. Another issue that frequently occurs in time series is missing values, due to system data record failure or unexpected data loss. Although there are numerous works about Gaussian AR time series with missing values, as far as we know, there does not exist any work addressing the issue of missing data for the heavy-tailed AR model. In this paper, we consider this issue for the first time, and propose an efficient framework for parameter estimation from incomplete heavy-tailed time series based on a stochastic approximation expectation maximization (SAEM) coupled with a Markov Chain Monte Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and easy to implement. The convergence of the proposed algorithm to a stationary point of the observed data likelihood is rigorously proved. Extensive simulations and real datasets analyses demonstrate the efficacy of the proposed framework.Comment: This is a companion document to a paper that is accepted to IEEE Transaction on Signal Processing 2019, complemented with the supplementary materia

Output feedback stable stochastic predictive control with hard control constraints

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the largest class of linear time invariant systems known to be amenable to stochastic stabilization under bounded control actions via output feedback stochastic predictive control

An ontology for carcinoma classification for clinical bioinformatics

There are a number of existing classifications and staging schemes for carcinomas, one of the most frequently used being the TNM classification. Such classifications represent classes of entities which exist at various anatomical levels of granularity. We argue that in order to apply such representations to the Electronic Health Records one needs sound ontologies which take into consideration the diversity of the domains which are involved in clinical bioinformatics. Here we outline a formal theory for addressing these issues in a way that the ontologies can be used to support inferences relating to entities which exist at different anatomical levels of granularity. Our case study is the colon carcinoma, one of the most common carcinomas prevalent within the European population

End-to-End Navigation in Unknown Environments using Neural Networks

We investigate how a neural network can learn perception actions loops for navigation in unknown environments. Specifically, we consider how to learn to navigate in environments populated with cul-de-sacs that represent convex local minima that the robot could fall into instead of finding a set of feasible actions that take it to the goal. Traditional methods rely on maintaining a global map to solve the problem of over coming a long cul-de-sac. However, due to errors induced from local and global drift, it is highly challenging to maintain such a map for long periods of time. One way to mitigate this problem is by using learning techniques that do not rely on hand engineered map representations and instead output appropriate control policies directly from their sensory input. We first demonstrate that such a problem cannot be solved directly by deep reinforcement learning due to the sparse reward structure of the environment. Further, we demonstrate that deep supervised learning also cannot be used directly to solve this problem. We then investigate network models that offer a combination of reinforcement learning and supervised learning and highlight the significance of adding fully differentiable memory units to such networks. We evaluate our networks on their ability to generalize to new environments and show that adding memory to such networks offers huge jumps in performanceComment: Workshop on Learning Perception and Control for Autonomous Flight: Safety, Memory and Efficiency, Robotics Science and Systems 201

Memory Augmented Control Networks

Planning problems in partially observable environments cannot be solved directly with convolutional networks and require some form of memory. But, even memory networks with sophisticated addressing schemes are unable to learn intelligent reasoning satisfactorily due to the complexity of simultaneously learning to access memory and plan. To mitigate these challenges we introduce the Memory Augmented Control Network (MACN). The proposed network architecture consists of three main parts. The first part uses convolutions to extract features and the second part uses a neural network-based planning module to pre-plan in the environment. The third part uses a network controller that learns to store those specific instances of past information that are necessary for planning. The performance of the network is evaluated in discrete grid world environments for path planning in the presence of simple and complex obstacles. We show that our network learns to plan and can generalize to new environments

13C-Methyl isocyanide as an NMR probe for cytochrome P450 active site

The cytochromes P450 (CYPs) play a central role in many biologically important oxidation reactions, including the metabolism of drugs and other xenobiotic compounds. Because they are often assayed as both drug targets and anti-targets, any tools that provide: (a) confirmation of active site binding and (b) structural data, would be of great utility, especially if data could be obtained in reasonably high throughput. To this end, we have developed an analog of the promiscuous heme ligand, cyanide,with a 13CH3-reporter attached. This 13C-methyl isocyanide ligand binds to bacterial (P450cam) and membrane-bound mammalian (CYP2B4) CYPs. It can be used in a rapid 1D experiment to identify binders, and provides a qualitative measure of structural changes in the active site

Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments

A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that TS is acyclic. In this article we consider the FEEDBACK VERTEX SET problem in tournaments. Here the input is a tournament T and an integer k, and the task is to determine whether T has a feedback vertex set of size at most k. We give a new algorithm for FEEDBACK VERTEX SET IN TOURNAMENTS. The running time of our algorithm is upper-bounded by O(1.6181^k + n^{O(1)}) and by O(1.466^n). Thus our algorithm simultaneously improves over the fastest known parameterized algorithm for the problem by Dom et al. running in time O(2^kk^{O(1)} + n^{O(1)}), and the fastest known exact exponential-time algorithm by Gaspers and Mnich with running time O(1.674^n). On the way to proving our main result we prove a strengthening of a special case of a graph partitioning theorem due to Bollobas and Scott. In particular we show that the vertices of any undirected m-edge graph of maximum degree d can be colored white or black in such a way that for each of the two colors, the number of edges with both endpoints of that color is between m/4-d/2 and m/4+d/2