3,006 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
Quantum discord in a spin system with symmetry breaking
We analyze the quantum discord Q throughout the low-temperature phase diagram
of the quantum XY model in transverse field. We first focus on the T=0
order-disorder quantum phase transition both in the symmetric ground state and
in the symmetry broken one. Besides it, we highlight how Q displays clear
anomalies also at a non critical value of the control parameter inside the
ordered phase, where the ground state is completely factorized. We evidence how
the phenomenon is in fact of collective nature and displays universal features.
We also study Q at finite temperature. We show that, close to the quantum phase
transition, Q exhibits quantum-classical crossover of the system with universal
scaling behavior. We evidence a non trivial pattern of thermal correlations
resulting from the factorization phenomenon.Comment: 9 pages, 9 figure, Contribution to the Festschrift volume in honour
of Vladimir Korepi
Nonclassical stochastic flows and continuous products
Contrary to the classical wisdom, processes with independent values (defined
properly) are much more diverse than white noise combined with Poisson point
processes, and product systems are much more diverse than Fock spaces.
This text is a survey of recent progress in constructing and investigating
nonclassical stochastic flows and continuous products of probability spaces and
Hilbert spaces.Comment: A survey, 126 pages. Version 3 (final): former Question 9d4 is
solved; 8a1 reformulated. Ref [41] added. For readability, sections are
reordered (123456..->142536..). Cosmetic changes, mostly in 1b, 2a, 3d, (4a7)
(v3 numbers) and Introductio
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