41,498 research outputs found
Reconstruction of Causal Networks by Set Covering
We present a method for the reconstruction of networks, based on the order of
nodes visited by a stochastic branching process. Our algorithm reconstructs a
network of minimal size that ensures consistency with the data. Crucially, we
show that global consistency with the data can be achieved through purely local
considerations, inferring the neighbourhood of each node in turn. The
optimisation problem solved for each individual node can be reduced to a Set
Covering Problem, which is known to be NP-hard but can be approximated well in
practice. We then extend our approach to account for noisy data, based on the
Minimum Description Length principle. We demonstrate our algorithms on
synthetic data, generated by an SIR-like epidemiological model.Comment: Under consideration for the ECML PKDD 2010 conferenc
Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
We propose a family of exactly solvable toy models for the AdS/CFT
correspondence based on a novel construction of quantum error-correcting codes
with a tensor network structure. Our building block is a special type of tensor
with maximal entanglement along any bipartition, which gives rise to an
isometry from the bulk Hilbert space to the boundary Hilbert space. The entire
tensor network is an encoder for a quantum error-correcting code, where the
bulk and boundary degrees of freedom may be identified as logical and physical
degrees of freedom respectively. These models capture key features of
entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi
formula and the negativity of tripartite information are obeyed exactly in many
cases. That bulk logical operators can be represented on multiple boundary
regions mimics the Rindler-wedge reconstruction of boundary operators from bulk
operators, realizing explicitly the quantum error-correcting features of
AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.Comment: 40 Pages + 25 Pages of Appendices. 38 figures. Typos and
bibliographic amendments and minor correction
When Causal Intervention Meets Adversarial Examples and Image Masking for Deep Neural Networks
Discovering and exploiting the causality in deep neural networks (DNNs) are
crucial challenges for understanding and reasoning causal effects (CE) on an
explainable visual model. "Intervention" has been widely used for recognizing a
causal relation ontologically. In this paper, we propose a causal inference
framework for visual reasoning via do-calculus. To study the intervention
effects on pixel-level features for causal reasoning, we introduce pixel-wise
masking and adversarial perturbation. In our framework, CE is calculated using
features in a latent space and perturbed prediction from a DNN-based model. We
further provide the first look into the characteristics of discovered CE of
adversarially perturbed images generated by gradient-based methods
\footnote{~~https://github.com/jjaacckkyy63/Causal-Intervention-AE-wAdvImg}.
Experimental results show that CE is a competitive and robust index for
understanding DNNs when compared with conventional methods such as
class-activation mappings (CAMs) on the Chest X-Ray-14 dataset for
human-interpretable feature(s) (e.g., symptom) reasoning. Moreover, CE holds
promises for detecting adversarial examples as it possesses distinct
characteristics in the presence of adversarial perturbations.Comment: Noted our camera-ready version has changed the title. "When Causal
Intervention Meets Adversarial Examples and Image Masking for Deep Neural
Networks" as the v3 official paper title in IEEE Proceeding. Please use it in
your formal reference. Accepted at IEEE ICIP 2019. Pytorch code has released
on https://github.com/jjaacckkyy63/Causal-Intervention-AE-wAdvIm
Successive Refinement with Decoder Cooperation and its Channel Coding Duals
We study cooperation in multi terminal source coding models involving
successive refinement. Specifically, we study the case of a single encoder and
two decoders, where the encoder provides a common description to both the
decoders and a private description to only one of the decoders. The decoders
cooperate via cribbing, i.e., the decoder with access only to the common
description is allowed to observe, in addition, a deterministic function of the
reconstruction symbols produced by the other. We characterize the fundamental
performance limits in the respective settings of non-causal, strictly-causal
and causal cribbing. We use a new coding scheme, referred to as Forward
Encoding and Block Markov Decoding, which is a variant of one recently used by
Cuff and Zhao for coordination via implicit communication. Finally, we use the
insight gained to introduce and solve some dual channel coding scenarios
involving Multiple Access Channels with cribbing.Comment: 55 pages, 15 figures, 8 tables, submitted to IEEE Transactions on
Information Theory. A shorter version submitted to ISIT 201
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