14,396 research outputs found
Bounded Expectations: Resource Analysis for Probabilistic Programs
This paper presents a new static analysis for deriving upper bounds on the
expected resource consumption of probabilistic programs. The analysis is fully
automatic and derives symbolic bounds that are multivariate polynomials of the
inputs. The new technique combines manual state-of-the-art reasoning techniques
for probabilistic programs with an effective method for automatic
resource-bound analysis of deterministic programs. It can be seen as both, an
extension of automatic amortized resource analysis (AARA) to probabilistic
programs and an automation of manual reasoning for probabilistic programs that
is based on weakest preconditions. As a result, bound inference can be reduced
to off-the-shelf LP solving in many cases and automatically-derived bounds can
be interactively extended with standard program logics if the automation fails.
Building on existing work, the soundness of the analysis is proved with respect
to an operational semantics that is based on Markov decision processes. The
effectiveness of the technique is demonstrated with a prototype implementation
that is used to automatically analyze 39 challenging probabilistic programs and
randomized algorithms. Experimental results indicate that the derived constant
factors in the bounds are very precise and even optimal for many programs
A computer algebra user interface manifesto
Many computer algebra systems have more than 1000 built-in functions, making
expertise difficult. Using mock dialog boxes, this article describes a proposed
interactive general-purpose wizard for organizing optional transformations and
allowing easy fine grain control over the form of the result even by amateurs.
This wizard integrates ideas including:
* flexible subexpression selection;
* complete control over the ordering of variables and commutative operands,
with well-chosen defaults;
* interleaving the choice of successively less main variables with applicable
function choices to provide detailed control without incurring a combinatorial
number of applicable alternatives at any one level;
* quick applicability tests to reduce the listing of inapplicable
transformations;
* using an organizing principle to order the alternatives in a helpful
manner;
* labeling quickly-computed alternatives in dialog boxes with a preview of
their results,
* using ellipsis elisions if necessary or helpful;
* allowing the user to retreat from a sequence of choices to explore other
branches of the tree of alternatives or to return quickly to branches already
visited;
* allowing the user to accumulate more than one of the alternative forms;
* integrating direct manipulation into the wizard; and
* supporting not only the usual input-result pair mode, but also the useful
alternative derivational and in situ replacement modes in a unified window.Comment: 38 pages, 12 figures, to be published in Communications in Computer
Algebr
A probabilistic algorithm to test local algebraic observability in polynomial time
The following questions are often encountered in system and control theory.
Given an algebraic model of a physical process, which variables can be, in
theory, deduced from the input-output behavior of an experiment? How many of
the remaining variables should we assume to be known in order to determine all
the others? These questions are parts of the \emph{local algebraic
observability} problem which is concerned with the existence of a non trivial
Lie subalgebra of the symmetries of the model letting the inputs and the
outputs invariant. We present a \emph{probabilistic seminumerical} algorithm
that proposes a solution to this problem in \emph{polynomial time}. A bound for
the necessary number of arithmetic operations on the rational field is
presented. This bound is polynomial in the \emph{complexity of evaluation} of
the model and in the number of variables. Furthermore, we show that the
\emph{size} of the integers involved in the computations is polynomial in the
number of variables and in the degree of the differential system. Last, we
estimate the probability of success of our algorithm and we present some
benchmarks from our Maple implementation.Comment: 26 pages. A Maple implementation is availabl
Exact linear modeling using Ore algebras
Linear exact modeling is a problem coming from system identification: Given a
set of observed trajectories, the goal is find a model (usually, a system of
partial differential and/or difference equations) that explains the data as
precisely as possible. The case of operators with constant coefficients is well
studied and known in the systems theoretic literature, whereas the operators
with varying coefficients were addressed only recently. This question can be
tackled either using Gr\"obner bases for modules over Ore algebras or by
following the ideas from differential algebra and computing in commutative
rings. In this paper, we present algorithmic methods to compute "most powerful
unfalsified models" (MPUM) and their counterparts with variable coefficients
(VMPUM) for polynomial and polynomial-exponential signals. We also study the
structural properties of the resulting models, discuss computer algebraic
techniques behind algorithms and provide several examples
Automatic Differentiation of Algorithms for Machine Learning
Automatic differentiation---the mechanical transformation of numeric computer
programs to calculate derivatives efficiently and accurately---dates to the
origin of the computer age. Reverse mode automatic differentiation both
antedates and generalizes the method of backwards propagation of errors used in
machine learning. Despite this, practitioners in a variety of fields, including
machine learning, have been little influenced by automatic differentiation, and
make scant use of available tools. Here we review the technique of automatic
differentiation, describe its two main modes, and explain how it can benefit
machine learning practitioners. To reach the widest possible audience our
treatment assumes only elementary differential calculus, and does not assume
any knowledge of linear algebra.Comment: 7 pages, 1 figur
Computing Dynamic Output Feedback Laws
The pole placement problem asks to find laws to feed the output of a plant
governed by a linear system of differential equations back to the input of the
plant so that the resulting closed-loop system has a desired set of
eigenvalues. Converting this problem into a question of enumerative geometry,
efficient numerical homotopy algorithms to solve this problem for general
Multi-Input-Multi-Output (MIMO) systems have been proposed recently. While
dynamic feedback laws offer a wider range of use, the realization of the output
of the numerical homotopies as a machine to control the plant in the time
domain has not been addressed before. In this paper we present symbolic-numeric
algorithms to turn the solution to the question of enumerative geometry into a
useful control feedback machine. We report on numerical experiments with our
publicly available software and illustrate its application on various control
problems from the literature.Comment: 20 pages, 3 figures; the software described in this paper is publicly
available via http://www.math.uic.edu/~jan/download.htm
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