1,581 research outputs found
On the Inability of Markov Models to Capture Criticality in Human Mobility
We examine the non-Markovian nature of human mobility by exposing the
inability of Markov models to capture criticality in human mobility. In
particular, the assumed Markovian nature of mobility was used to establish a
theoretical upper bound on the predictability of human mobility (expressed as a
minimum error probability limit), based on temporally correlated entropy. Since
its inception, this bound has been widely used and empirically validated using
Markov chains. We show that recurrent-neural architectures can achieve
significantly higher predictability, surpassing this widely used upper bound.
In order to explain this anomaly, we shed light on several underlying
assumptions in previous research works that has resulted in this bias. By
evaluating the mobility predictability on real-world datasets, we show that
human mobility exhibits scale-invariant long-range correlations, bearing
similarity to a power-law decay. This is in contrast to the initial assumption
that human mobility follows an exponential decay. This assumption of
exponential decay coupled with Lempel-Ziv compression in computing Fano's
inequality has led to an inaccurate estimation of the predictability upper
bound. We show that this approach inflates the entropy, consequently lowering
the upper bound on human mobility predictability. We finally highlight that
this approach tends to overlook long-range correlations in human mobility. This
explains why recurrent-neural architectures that are designed to handle
long-range structural correlations surpass the previously computed upper bound
on mobility predictability
Bayesian inference of CMB gravitational lensing
The Planck satellite, along with several ground based telescopes, have mapped
the cosmic microwave background (CMB) at sufficient resolution and
signal-to-noise so as to allow a detection of the subtle distortions due to the
gravitational influence of the intervening matter distribution. A natural
modeling approach is to write a Bayesian hierarchical model for the lensed CMB
in terms of the unlensed CMB and the lensing potential. So far there has been
no feasible algorithm for inferring the posterior distribution of the lensing
potential from the lensed CMB map. We propose a solution that allows efficient
Markov Chain Monte Carlo sampling from the joint posterior of the lensing
potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique.
The main conceptual step in the solution is a re-parameterization of CMB
lensing in terms of the lensed CMB and the "inverse lensing" potential. We
demonstrate a fast implementation on simulated data including noise and a sky
cut, that uses a further acceleration based on a very mild approximation of the
inverse lensing potential. We find that the resulting Markov Chain has short
correlation lengths and excellent convergence properties, making it promising
for application to high resolution CMB data sets of the future
The Pair-Replica-Mean-Field Limit for Intensity-based Neural Networks
Replica-mean-field models have been proposed to decipher the activity of
neural networks via a multiply-and-conquer approach. In this approach, one
considers limit networks made of infinitely many replicas with the same basic
neural structure as that of the network of interest, but exchanging spikes in a
randomized manner. The key point is that these replica-mean-field networks are
tractable versions that retain important features of the finite structure of
interest. To date, the replica framework has been discussed for first-order
models, whereby elementary replica constituents are single neurons with
independent Poisson inputs. Here, we extend this replica framework to allow
elementary replica constituents to be composite objects, namely, pairs of
neurons. As they include pairwise interactions, these pair-replica models
exhibit non-trivial dependencies in their stationary dynamics, which cannot be
captured by first-order replica models. Our contributions are two-fold:
We analytically characterize the stationary dynamics of a pair of
intensity-based neurons with independent Poisson input. This analysis involves
the reduction of a boundary-value problem related to a two-dimensional
transport equation to a system of Fredholm integral equations---a result of
independent interest. We analyze the set of consistency equations
determining the full network dynamics of certain replica limits. These limits
are those for which replica constituents, be they single neurons or pairs of
neurons, form a partition of the network of interest. Both analyses are
numerically validated by computing input/output transfer functions for neuronal
pairs and by computing the correlation structure of certain pair-dominated
network dynamics.Comment: 40 pages, 6 figure
Active Learning of Continuous-time Bayesian Networks through Interventions
We consider the problem of learning structures and parameters of
Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal
experimental resources. In practice, the cost of generating experimental data
poses a bottleneck, especially in the natural and social sciences. A popular
approach to overcome this is Bayesian optimal experimental design (BOED).
However, BOED becomes infeasible in high-dimensional settings, as it involves
integration over all possible experimental outcomes. We propose a novel
criterion for experimental design based on a variational approximation of the
expected information gain. We show that for CTBNs, a semi-analytical expression
for this criterion can be calculated for structure and parameter learning. By
doing so, we can replace sampling over experimental outcomes by solving the
CTBNs master-equation, for which scalable approximations exist. This alleviates
the computational burden of sampling possible experimental outcomes in
high-dimensions. We employ this framework in order to recommend interventional
sequences. In this context, we extend the CTBN model to conditional CTBNs in
order to incorporate interventions. We demonstrate the performance of our
criterion on synthetic and real-world data.Comment: Accepted at ICML202
Beyond the Spectral Theorem: Spectrally Decomposing Arbitrary Functions of Nondiagonalizable Operators
Nonlinearities in finite dimensions can be linearized by projecting them into
infinite dimensions. Unfortunately, often the linear operator techniques that
one would then use simply fail since the operators cannot be diagonalized. This
curse is well known. It also occurs for finite-dimensional linear operators. We
circumvent it by developing a meromorphic functional calculus that can
decompose arbitrary functions of nondiagonalizable linear operators in terms of
their eigenvalues and projection operators. It extends the spectral theorem of
normal operators to a much wider class, including circumstances in which poles
and zeros of the function coincide with the operator spectrum. By allowing the
direct manipulation of individual eigenspaces of nonnormal and
nondiagonalizable operators, the new theory avoids spurious divergences. As
such, it yields novel insights and closed-form expressions across several areas
of physics in which nondiagonalizable dynamics are relevant, including
memoryful stochastic processes, open non unitary quantum systems, and
far-from-equilibrium thermodynamics.
The technical contributions include the first full treatment of arbitrary
powers of an operator. In particular, we show that the Drazin inverse,
previously only defined axiomatically, can be derived as the negative-one power
of singular operators within the meromorphic functional calculus and we give a
general method to construct it. We provide new formulae for constructing
projection operators and delineate the relations between projection operators,
eigenvectors, and generalized eigenvectors.
By way of illustrating its application, we explore several, rather distinct
examples.Comment: 29 pages, 4 figures, expanded historical citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/bst.ht
Infinite cycles in the random stirring model on trees
We prove that, in the random stirring model of parameter T on an infinite
rooted tree each of whose vertices has at least two offspring, infinite cycles
exist almost surely, provided that T is sufficiently high.
In the appendices, the bound on degree above which the result holds is
improved slightly.Comment: 23 pages, two figure
Examining the Limits of Predictability of Human Mobility
We challenge the upper bound of human-mobility predictability that is widely used to corroborate the accuracy of mobility prediction models. We observe that extensions of recurrent-neural network architectures achieve significantly higher prediction accuracy, surpassing this upper bound. Given this discrepancy, the central objective of our work is to show that the methodology behind the estimation of the predictability upper bound is erroneous and identify the reasons behind this discrepancy. In order to explain this anomaly, we shed light on several underlying assumptions that have contributed to this bias. In particular, we highlight the consequences of the assumed Markovian nature of human-mobility on deriving this upper bound on maximum mobility predictability. By using several statistical tests on three real-world mobility datasets, we show that human mobility exhibits scale-invariant long-distance dependencies, contrasting with the initial Markovian assumption. We show that this assumption of exponential decay of information in mobility trajectories, coupled with the inadequate usage of encoding techniques results in entropy inflation, consequently lowering the upper bound on predictability. We highlight that the current upper bound computation methodology based on Fano’s inequality tends to overlook the presence of long-range structural correlations inherent to mobility behaviors and we demonstrate its significance using an alternate encoding scheme. We further show the manifestation of not accounting for these dependencies by probing the mutual information decay in mobility trajectories. We expose the systematic bias that culminates into an inaccurate upper bound and further explain as to why the recurrent-neural architectures, designed to handle long-range structural correlations, surpass this upper limit on human mobility predictability
Undesired monetary policy effects in a bubbly world
Stock market bubbles arise as a joint monetary and financial phenomenon. We assess the potential of monetary policy in mitigating the onset of bubbles by means of a Markov-switching Bayesian Vector Autoregression model estimated on US 1960-2019 data. Bubbles are detected and dated from the regime-specific interplay among asset prices, fundamental values, and monetary policy shocks. We rationalize the empirical evidence with an Overlapping Generations model, able to generate a bubbly scenario with shifts in monetary policy, and where agents form beliefs over transition dynamics. By matching the VAR impulse responses, we find that procyclicality and financial instability align with high equity premia and the presence of asset price bubbles. Monetary policy tightening, by increasing real rates, is ineffective in deflating bubble episodes
- …