8,176 research outputs found
HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web
When users interact with the Web today, they leave sequential digital trails
on a massive scale. Examples of such human trails include Web navigation,
sequences of online restaurant reviews, or online music play lists.
Understanding the factors that drive the production of these trails can be
useful for e.g., improving underlying network structures, predicting user
clicks or enhancing recommendations. In this work, we present a general
approach called HypTrails for comparing a set of hypotheses about human trails
on the Web, where hypotheses represent beliefs about transitions between
states. Our approach utilizes Markov chain models with Bayesian inference. The
main idea is to incorporate hypotheses as informative Dirichlet priors and to
leverage the sensitivity of Bayes factors on the prior for comparing hypotheses
with each other. For eliciting Dirichlet priors from hypotheses, we present an
adaption of the so-called (trial) roulette method. We demonstrate the general
mechanics and applicability of HypTrails by performing experiments with (i)
synthetic trails for which we control the mechanisms that have produced them
and (ii) empirical trails stemming from different domains including website
navigation, business reviews and online music played. Our work expands the
repertoire of methods available for studying human trails on the Web.Comment: Published in the proceedings of WWW'1
Hierarchical Implicit Models and Likelihood-Free Variational Inference
Implicit probabilistic models are a flexible class of models defined by a
simulation process for data. They form the basis for theories which encompass
our understanding of the physical world. Despite this fundamental nature, the
use of implicit models remains limited due to challenges in specifying complex
latent structure in them, and in performing inferences in such models with
large data sets. In this paper, we first introduce hierarchical implicit models
(HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian
modeling, thereby defining models via simulators of data with rich hidden
structure. Next, we develop likelihood-free variational inference (LFVI), a
scalable variational inference algorithm for HIMs. Key to LFVI is specifying a
variational family that is also implicit. This matches the model's flexibility
and allows for accurate approximation of the posterior. We demonstrate diverse
applications: a large-scale physical simulator for predator-prey populations in
ecology; a Bayesian generative adversarial network for discrete data; and a
deep implicit model for text generation.Comment: Appears in Neural Information Processing Systems, 201
Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis
A frequentist asymptotic expansion method for error estimation is employed
for a network of gravitational wave detectors to assess the amount of
information that can be extracted from gravitational wave observations.
Mathematically we derive lower bounds in the errors that any parameter
estimator will have in the absence of prior knowledge to distinguish between
the post-Einsteinian (ppE) description of coalescing binary systems and that of
general relativity. When such errors are smaller than the parameter value,
there is possibility to detect these violations from GR. A parameter space with
inclusion of dominant dephasing ppE parameters is used for a study
of first- and second-order (co)variance expansions, focusing on the inspiral
stage of a nonspinning binary system of zero eccentricity detectible through
Adv. LIGO and Adv. Virgo. Our procedure is an improvement of the Cram\'{e}r-Rao
Lower Bound. When Bayesian errors are lower than our bound it means that they
depend critically on the priors. The analysis indicates the possibility of
constraining deviations from GR in inspiral SNR () regimes
that are achievable in upcoming scientific runs (GW150914 had an inspiral SNR
). The errors on also increase errors of other parameters such
as the chirp mass and symmetric mass ratio . Application is
done to existing alternative theories of gravity, which include modified
dispersion relation of the waveform, non-spinning models of quadratic modified
gravity, and dipole gravitational radiation (i.e., Brans-Dicke type)
modifications.Comment: 15 pages, 9 figure
Gravitational Wave Tests of General Relativity with the Parameterized Post-Einsteinian Framework
Gravitational wave astronomy has tremendous potential for studying extreme
astrophysical phenomena and exploring fundamental physics. The waves produced
by binary black hole mergers will provide a pristine environment in which to
study strong field, dynamical gravity. Extracting detailed information about
these systems requires accurate theoretical models of the gravitational wave
signals. If gravity is not described by General Relativity, analyses that are
based on waveforms derived from Einstein's field equations could result in
parameter biases and a loss of detection efficiency. A new class of
"parameterized post-Einsteinian" (ppE) waveforms has been proposed to cover
this eventuality. Here we apply the ppE approach to simulated data from a
network of advanced ground based interferometers (aLIGO/aVirgo) and from a
future spaced based interferometer (LISA). Bayesian inference and model
selection are used to investigate parameter biases, and to determine the level
at which departures from general relativity can be detected. We find that in
some cases the parameter biases from assuming the wrong theory can be severe.
We also find that gravitational wave observations will beat the existing bounds
on deviations from general relativity derived from the orbital decay of binary
pulsars by a large margin across a wide swath of parameter space.Comment: 16 pages, 10 figures. Modified in response to referee comment
Modularity and the predictive mind
Modular approaches to the architecture of the mind claim that some mental mechanisms, such as sensory input processes, operate in special-purpose subsystems that are functionally independent from the rest of the mind. This assumption of modularity seems to be in tension with recent claims that the mind has a predictive architecture. Predictive approaches propose that both sensory processing and higher-level processing are part of the same Bayesian information-processing hierarchy, with no clear boundary between perception and cognition. Furthermore, it is not clear how any part of the predictive architecture could be functionally independent, given that each level of the hierarchy is influenced by the level above. Both the assumption of continuity across the predictive architecture and the seeming non-isolability of parts of the predictive architecture seem to be at odds with the modular approach. I explore and ultimately reject the predictive approach’s apparent commitments to continuity and non-isolation. I argue that predictive architectures can be modular architectures, and that we should in fact expect predictive architectures to exhibit some form of modularity
Designing and testing inflationary models with Bayesian networks
Even simple inflationary scenarios have many free parameters. Beyond the
variables appearing in the inflationary action, these include dynamical initial
conditions, the number of fields, and couplings to other sectors. These
quantities are often ignored but cosmological observables can depend on the
unknown parameters. We use Bayesian networks to account for a large set of
inflationary parameters, deriving generative models for the primordial spectra
that are conditioned on a hierarchical set of prior probabilities describing
the initial conditions, reheating physics, and other free parameters. We use
--quadratic inflation as an illustrative example, finding that the number
of -folds between horizon exit for the pivot scale and the end of
inflation is typically the most important parameter, even when the number of
fields, their masses and initial conditions are unknown, along with possible
conditional dependencies between these parameters.Comment: 24 pages, 9 figures, 1 table; discussion update
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
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