Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic inference problem, and allows us to calculate any “optimal” estimate of the state. Unfortunately, for most real-world problems, the optimal Bayesian recursion is intractable and approximate solutions must be used. Within the space of approximate solutions, the extended Kalman filter (EKF) has become one of the most widely used algorithms with applications in state, parameter and dual estimation. Unfortunately, the EKF is based on a sub-optimal implementation of the recursive Bayesian estimation framework applied to Gaussian random variables. This can seriously affect the accuracy or even lead to divergence of any inference system that is based on the EKF or that uses the EKF as a component part. Recently a number of related novel, more accurate and theoretically better motivated algorithmic alternatives to the EKF have surfaced in the literature, with specific application to state estimation for automatic control. We have extended these algorithms, all based on derivativeless deterministic sampling based approximations of the relevant Gaussian statistics, to a family of algorithms called Sigma-Point Kalman Filters (SPKF). Furthermore, we successfully expanded the use of this group of algorithms (SPKFs) within the general field of probabilistic inference and machine learning, both as stand-alone filters and as subcomponents of more powerful sequential Monte Carlo methods (particle filters). We have consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.

/pdf/sigma-point-kalman-filters-for-probabilistic-inference-in-1affrc62j6.pdf

Sigma-point kalman filters for probabilistic inference in dynamic state-space models

https://superfund.berkeley.edu/pdf/92.pdf

Epidemiology of Myelodysplastic Syndromes and Chronic Myeloproliferative Disorders in the United States, 2001-2004, Using Data From the NAACCR and SEER Programs

Diagnosis and treatment of primary myelodysplastic syndromes in adults: recommendations from the European LeukemiaNet

Monads have become very popular for structuring functional programs since Wadler introduced their use in 1990. In particular, libraries of combinators are often based on a monadic type. Such libraries share (in part) a common interface, from which numerous benefits flow, such as the possibility to write generic code which works together with any library. But, several interesting and useful libraries are fundamentally incompatible with the monadic interface. In this paper I propose a generalisation of monads, which I call arrows, with significantly wider applicability. The paper shows how many of the techniques of monadic programming generalise to the new setting, and gives examples to show that the greater generality is useful. In particular, three non-monadic libraries for efficient parsing, building graphical user interfaces, and programming active web pages fit naturally into the new framework.

Generalising monads to arrows

A probabilistic framework, called Sigma-point Kalman Filters (SPKF) was applied to the problem domain addressed by the extended Kalman Filter (EKF). SPKF methods are superior to the standard EKF based estimation approaches, as an SPKF achieves second-order or higher accuracy. The SPKF has also been applied to the integrated navigation problem as it relates to unmanned aerial vehicle (UAV) autonomy. The SPKF-based sensor latency compensation technique is used to demonstrate the lagged GPS measurements.

/pdf/sigma-point-kalman-filters-for-nonlinear-estimation-and-3h5o0hche0.pdf

Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor Fusion: Applications to Integrated Navigation

Object-oriented, concurrent, and event-based programming models provide a natural framework in which to express the behavior of distributed and embedded software systems. However, contemporary programming languages still base their I/O primitives on a model in which the environment is assumed to be centrally controlled and synchronous, and interactions with the environment carried out through blocking subroutine calls. The gap between this view and the natural asynchrony of the real world has made event-based programming a complex and error-prone activity, despite recent focus on event-based frameworks and middleware. In thin paper we present a consistent model of event-based concurrency, centered around the notion of reactive objects. This model relieves the object-oriented paradigm from the idea of transparent blocking, and naturally enforces reactivity and state consistency We illustrate our point by a program example that offers substantial improvements in size and simplicity over a corresponding Java-based solution.

http://ieeexplore.ieee.org/iel5/7870/21665/01003682.pdf

Reactive objects

Monitoring ethanol exposure in a clinical setting by analysis of blood, breath, saliva, and urine.

Monitoring ethanol exposure in a clinical setting by analysis of blood, breath, saliva, and urine

The powerful abstraction mechanisms of functional programming languages provide the means to develop domain-specific programming languages within the language itself Typically, this is realised by designing a set of combinators (higher-order reusable programs) for an application area, and by constructing individual applications by combining and coordinating individual combinators This paper is concerned with a successful example of such an embedded programming language, namely Fudgets, a library of combinators for building graphical user interfaces in the lazy functional language Haskell The Fudget library has been used to build a number of substantial applications, including a web browser and a proof editor interface to a proof checker for constructive type theory This paper develops a semantic theory for the non-deterministic stream processors that are at the heart of the Fudget concept The interaction of two features of stream processors makes the development of such a semantic theory problematic: (i) the sharing of computation provided by the lazy evaluation mechanism of the underlying host language, and (ii) the addition of non-deterministic choice needed to handle the natural concurrency that reactive applications entail

We demonstrate that this combination of features in a higher-order functional language can be tamed to provide a tractable semantic theory and induction principles suitable for reasoning about contextual equivalence of Fudgets

Erratic Fudgets: A Semantic Theory for an Embedded Coordination Language

The main result of this thesis is a method for writing programs with graphical user interfaces in purely functional languages The method is based on a new abstraction called the fudget The method makes good use of key abstraction powers of functional languages, such as higher order functions and parametric polymorphism The Fudget concept is defined in terms of the simpler concept of stream processors, which can be seen as a simple, but practically useful incarnation of the process concept Programs based on fudgets and stream processors are networks of communicating processes that are built hierarchically, using combinators Communication is type safe The basic combinators provide serial compositions, parallel compositions, and loops A key difference between previous work on stream processing functions and our approach is that we deliberately abstract away from the streams We obtain a system that can be implemented deterministically, entirely within a purely functional language, but which also makes it possible to take advantage of parallel evaluation and indeterminism, where such is available within the functional language The purely functional approach makes processes first class values and makes it easy to express process cloning and process migration The practical viability of the approach is demonstrated by the Fudget library, which is an implementation of a graphical user interface toolkit in the purely functional language Haskell, together with a number of small an large applications that have been implemented on top of the library In addition to GUI programming, fudgets are suitable for other forms of concurrent I/O programming We demonstrate how client/server based applications can be we written, with type safe communication between client and server We show a web browser as an example where GUI programming and network communication come together We view fudgets as one example of a more general combinator-based approach to promote the idea that a functional language together with combinator libraries is a good alternative to using less expressive languages propped by application-specific tools We describe a set of combinators, reminiscent of parsing combinators, for building syntax-directed editors

Fudgets - Purely Functional Processes with applications to Graphical User Interfaces

We present a three-layered semantics of Timber, a language designed for programming real-time systems in a reactive, object-oriented style. The innermost layer amounts to a traditional deterministic, pure, functional language, around which we formulate a middle layer of concurrent objects, in terms of a monadic transition semantics. The outermost layer, where the language is married to deadline-driven scheduling theory, is where we define message ordering and CPU allocation to actions. Our main contributions are a formalized notion of a time-constrained reaction, and a demonstration of how scheduling theory, process calculii, and the lambda calculus can be jointly applied to obtain a direct and succinct semantics of a complex, real-world programming language with well-defined real-time behavior.

Magnus Carlsson

Papers

Reactive objects

Monitoring ethanol exposure in a clinical setting by analysis of blood, breath, saliva, and urine

Erratic Fudgets: A Semantic Theory for an Embedded Coordination Language

Fudgets - Purely Functional Processes with applications to Graphical User Interfaces

The Semantic Layers of Timber