2,292 research outputs found
Learning and Designing Stochastic Processes from Logical Constraints
Stochastic processes offer a flexible mathematical formalism to model and
reason about systems. Most analysis tools, however, start from the premises
that models are fully specified, so that any parameters controlling the
system's dynamics must be known exactly. As this is seldom the case, many
methods have been devised over the last decade to infer (learn) such parameters
from observations of the state of the system. In this paper, we depart from
this approach by assuming that our observations are {\it qualitative}
properties encoded as satisfaction of linear temporal logic formulae, as
opposed to quantitative observations of the state of the system. An important
feature of this approach is that it unifies naturally the system identification
and the system design problems, where the properties, instead of observations,
represent requirements to be satisfied. We develop a principled statistical
estimation procedure based on maximising the likelihood of the system's
parameters, using recent ideas from statistical machine learning. We
demonstrate the efficacy and broad applicability of our method on a range of
simple but non-trivial examples, including rumour spreading in social networks
and hybrid models of gene regulation
Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Open accessThis paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. Optimal model parameter values are obtained from ïŹts to consecutive daily 2-year period returns of S&P500 index over [1950â2016], generating 33-time series estimations. Through an econometric model,the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk
Globally Continuous and Non-Markovian Crowd Activity Analysis from Videos
Automatically recognizing activities in video is a classic problem in vision and helps to understand behaviors, describe scenes and detect anomalies. We propose an unsupervised method for such purposes. Given video data, we discover recurring activity patterns that appear, peak, wane and disappear over time. By using non-parametric Bayesian methods, we learn coupled spatial and temporal patterns with minimum prior knowledge. To model the temporal changes of patterns, previous works compute Markovian progressions or locally continuous motifs whereas we model time in a globally continuous and non-Markovian way. Visually, the patterns depict flows of major activities. Temporally, each pattern has its own unique appearance-disappearance cycles. To compute compact pattern representations, we also propose a hybrid sampling method. By combining these patterns with detailed environment information, we interpret the semantics of activities and report anomalies. Also, our method fits data better and detects anomalies that were difficult to detect previously
Cleaning sky survey databases using Hough Transform and Renewal String approaches
Large astronomical databases obtained from sky surveys such as the
SuperCOSMOS Sky Survey (SSS) invariably suffer from spurious records coming
from artefactual effects of the telescope, satellites and junk objects in orbit
around earth and physical defects on the photographic plate or CCD. Though
relatively small in number these spurious records present a significant problem
in many situations where they can become a large proportion of the records
potentially of interest to a given astronomer. Accurate and robust techniques
are needed for locating and flagging such spurious objects, and we are
undertaking a programme investigating the use of machine learning techniques in
this context. In this paper we focus on the four most common causes of unwanted
records in the SSS: satellite or aeroplane tracks, scratches, fibres and other
linear phenomena introduced to the plate, circular halos around bright stars
due to internal reflections within the telescope and diffraction spikes near to
bright stars. Appropriate techniques are developed for the detection of each of
these. The methods are applied to the SSS data to develop a dataset of spurious
object detections, along with confidence measures, which can allow these
unwanted data to be removed from consideration. These methods are general and
can be adapted to other astronomical survey data.Comment: Accepted for MNRAS. 17 pages, latex2e, uses mn2e.bst, mn2e.cls,
md706.bbl, shortbold.sty (all included). All figures included here as low
resolution jpegs. A version of this paper including the figures can be
downloaded from http://www.anc.ed.ac.uk/~amos/publications.html and more
details on this project can be found at
http://www.anc.ed.ac.uk/~amos/sattrackres.htm
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