492 research outputs found
Semantic Information G Theory and Logical Bayesian Inference for Machine Learning
An important problem with machine learning is that when label number n\u3e2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic
Minimum and maximum entropy distributions for binary systems with known means and pairwise correlations
Maximum entropy models are increasingly being used to describe the collective
activity of neural populations with measured mean neural activities and
pairwise correlations, but the full space of probability distributions
consistent with these constraints has not been explored. We provide upper and
lower bounds on the entropy for the {\em minimum} entropy distribution over
arbitrarily large collections of binary units with any fixed set of mean values
and pairwise correlations. We also construct specific low-entropy distributions
for several relevant cases. Surprisingly, the minimum entropy solution has
entropy scaling logarithmically with system size for any set of first- and
second-order statistics consistent with arbitrarily large systems. We further
demonstrate that some sets of these low-order statistics can only be realized
by small systems. Our results show how only small amounts of randomness are
needed to mimic low-order statistical properties of highly entropic
distributions, and we discuss some applications for engineered and biological
information transmission systems.Comment: 34 pages, 7 figure
Real-Time Source Independent Quantum Random Number Generator with Squeezed States
Random numbers are a fundamental ingredient for many applications including
simulation, modelling and cryptography. Sound random numbers should be
independent and uniformly distributed. Moreover, for cryptographic applications
they should also be unpredictable. We demonstrate a real-time self-testing
source independent quantum random number generator (QRNG) that uses squeezed
light as source. We generate secure random numbers by measuring the quadratures
of the electromagnetic field without making any assumptions on the source; only
the detection device is trusted. We use a homodyne detection to alternatively
measure the Q and P conjugate quadratures of our source. Using the entropic
uncertainty relation, measurements on P allow us to estimate a bound on the
min-entropy of Q conditioned on any classical or quantum side information that
a malicious eavesdropper may detain. This bound gives the minimum number of
secure bits we can extract from the Q measurement. We discuss the performance
of different estimators for this bound. We operate this QRNG with a squeezed
state and we compare its performance with a QRNG using thermal states. The
real-time bit rate was 8.2 kb/s when using the squeezed source and between
5.2-7.2 kb/s when the thermal state source was used.Comment: 11 pages, 9 figure
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