6,543 research outputs found
Deriving Probability Density Functions from Probabilistic Functional Programs
The probability density function of a probability distribution is a
fundamental concept in probability theory and a key ingredient in various
widely used machine learning methods. However, the necessary framework for
compiling probabilistic functional programs to density functions has only
recently been developed. In this work, we present a density compiler for a
probabilistic language with failure and both discrete and continuous
distributions, and provide a proof of its soundness. The compiler greatly
reduces the development effort of domain experts, which we demonstrate by
solving inference problems from various scientific applications, such as
modelling the global carbon cycle, using a standard Markov chain Monte Carlo
framework
Random Modulo: A new processor cache design for real-time critical systems
Cache memories have a huge impact on software's worst-case execution time (WCET). While enabling the seamless use of caches is key to provide the increasing levels of (guaranteed) performance required by automotive software, caches complicate timing analysis. In the context of Measurement-Based Probabilistic Timing Analysis (MBPTA) - a promising technique to ease timing analyis of complex hardware - we propose Random Modulo (RM), a new cache design that provides the probabilistic behavior required by MBPTA and with the following advantages over existing MBPTA-compliant cache designs: (i) an outstanding reduction in WCET estimates, (ii) lower latency and area overhead, and (iii) competitive average performance w.r.t conventional caches.Peer ReviewedPostprint (author's final draft
Practical probabilistic programming with monads
The machine learning community has recently shown a lot of interest in practical probabilistic programming systems that target the problem of Bayesian inference. Such systems come in different forms, but they all express probabilistic models as computational processes using syntax resembling programming languages. In the functional programming community monads are known to offer a convenient and elegant abstraction for programming with probability distributions, but their use is often limited to very simple inference problems. We show that it is possible to use the monad abstraction to construct probabilistic models for machine learning, while still offering good performance of inference in challenging models. We use a GADT as an underlying representation of a probability distribution and apply Sequential Monte Carlo-based methods to achieve efficient inference. We define a formal semantics via measure theory. We demonstrate a clean and elegant implementation that achieves performance comparable with Anglican, a state-of-the-art probabilistic programming system.The first author is supported by EPSRC and the Cambridge Trust.This is the author accepted manuscript. The final version is available from ACM via http://dx.doi.org/10.1145/2804302.280431
Formal verification of higher-order probabilistic programs
Probabilistic programming provides a convenient lingua franca for writing
succinct and rigorous descriptions of probabilistic models and inference tasks.
Several probabilistic programming languages, including Anglican, Church or
Hakaru, derive their expressiveness from a powerful combination of continuous
distributions, conditioning, and higher-order functions. Although very
important for practical applications, these combined features raise fundamental
challenges for program semantics and verification. Several recent works offer
promising answers to these challenges, but their primary focus is on semantical
issues.
In this paper, we take a step further and we develop a set of program logics,
named PPV, for proving properties of programs written in an expressive
probabilistic higher-order language with continuous distributions and operators
for conditioning distributions by real-valued functions. Pleasingly, our
program logics retain the comfortable reasoning style of informal proofs thanks
to carefully selected axiomatizations of key results from probability theory.
The versatility of our logics is illustrated through the formal verification of
several intricate examples from statistics, probabilistic inference, and
machine learning. We further show the expressiveness of our logics by giving
sound embeddings of existing logics. In particular, we do this in a parametric
way by showing how the semantics idea of (unary and relational) TT-lifting can
be internalized in our logics. The soundness of PPV follows by interpreting
programs and assertions in quasi-Borel spaces (QBS), a recently proposed
variant of Borel spaces with a good structure for interpreting higher order
probabilistic programs
Speakable in quantum mechanics: babbling on
This paper consists of a short version of the derivation of the
intuitionistic quantum logic L_QM (which was originally introduced by Caspers,
Heunen, Landsman and Spitters). The elaboration consists of extending this
logic to a classical logic CL_QM. Some first steps are then taken towards
setting up a probabilistic framework based on CL_QM in terms of R\'enyi's
conditional probability spaces. Comparisons are then made with the traditional
framework for quantum probabilities.Comment: In Proceedings QPL 2012, arXiv:1407.842
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