54,186 research outputs found
Causal Inference by Stochastic Complexity
The algorithmic Markov condition states that the most likely causal direction
between two random variables X and Y can be identified as that direction with
the lowest Kolmogorov complexity. Due to the halting problem, however, this
notion is not computable.
We hence propose to do causal inference by stochastic complexity. That is, we
propose to approximate Kolmogorov complexity via the Minimum Description Length
(MDL) principle, using a score that is mini-max optimal with regard to the
model class under consideration. This means that even in an adversarial
setting, such as when the true distribution is not in this class, we still
obtain the optimal encoding for the data relative to the class.
We instantiate this framework, which we call CISC, for pairs of univariate
discrete variables, using the class of multinomial distributions. Experiments
show that CISC is highly accurate on synthetic, benchmark, as well as
real-world data, outperforming the state of the art by a margin, and scales
extremely well with regard to sample and domain sizes
Uncertainty Reduction for Stochastic Processes on Complex Networks
Many real-world systems are characterized by stochastic dynamical rules where
a complex network of interactions among individual elements probabilistically
determines their state. Even with full knowledge of the network structure and
of the stochastic rules, the ability to predict system configurations is
generally characterized by a large uncertainty. Selecting a fraction of the
nodes and observing their state may help to reduce the uncertainty about the
unobserved nodes. However, choosing these points of observation in an optimal
way is a highly nontrivial task, depending on the nature of the stochastic
process and on the structure of the underlying interaction pattern. In this
paper, we introduce a computationally efficient algorithm to determine
quasioptimal solutions to the problem. The method leverages network sparsity to
reduce computational complexity from exponential to almost quadratic, thus
allowing the straightforward application of the method to mid-to-large-size
systems. Although the method is exact only for equilibrium stochastic processes
defined on trees, it turns out to be effective also for out-of-equilibrium
processes on sparse loopy networks.Comment: 5 pages, 2 figures + Supplemental Material. A python implementation
of the algorithm is available at
https://github.com/filrad/Maximum-Entropy-Samplin
Parallel implementation of stochastic simulation for large-scale cellular processes
Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes
Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks
The stochastic block model (SBM) is a flexible probabilistic tool that can be
used to model interactions between clusters of nodes in a network. However, it
does not account for interactions of time varying intensity between clusters.
The extension of the SBM developed in this paper addresses this shortcoming
through a temporal partition: assuming interactions between nodes are recorded
on fixed-length time intervals, the inference procedure associated with the
model we propose allows to cluster simultaneously the nodes of the network and
the time intervals. The number of clusters of nodes and of time intervals, as
well as the memberships to clusters, are obtained by maximizing an exact
integrated complete-data likelihood, relying on a greedy search approach.
Experiments on simulated and real data are carried out in order to assess the
proposed methodology
Statistical and Computational Tradeoffs in Stochastic Composite Likelihood
Maximum likelihood estimators are often of limited practical use due to the
intensive computation they require. We propose a family of alternative
estimators that maximize a stochastic variation of the composite likelihood
function. Each of the estimators resolve the computation-accuracy tradeoff
differently, and taken together they span a continuous spectrum of
computation-accuracy tradeoff resolutions. We prove the consistency of the
estimators, provide formulas for their asymptotic variance, statistical
robustness, and computational complexity. We discuss experimental results in
the context of Boltzmann machines and conditional random fields. The
theoretical and experimental studies demonstrate the effectiveness of the
estimators when the computational resources are insufficient. They also
demonstrate that in some cases reduced computational complexity is associated
with robustness thereby increasing statistical accuracy.Comment: 30 pages, 97 figures, 2 author
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