76 research outputs found
Exchangeability and Realizability: De Finetti Theorems on Graphs
A classic result in probability theory known as de Finetti\u27s theorem states that exchangeable random variables are equivalent to a mixture of distributions where each distribution is determined by an i.i.d. sequence of random variables (an "i.i.d. mix"). Motivated by a recent application and more generally by the relationship of local vs. global correlation in randomized rounding, we study weaker notions of exchangeability that still imply the conclusion of de Finetti\u27s theorem. We say that a bivariate distribution rho is G-realizable for a graph G if there exists a joint distribution of random variables on the vertices such that the marginal distribution on each edge equals rho.
We first characterize completely the G-realizable distributions for all symmetric/arc-transitive graphs G. Our main results are forms of de Finetti\u27s theorem for general graphs, based on spectral properties. Let lambda_1(G) >= ... >= lambda_n(G) denote the eigenvalues of the adjacency matrix of G.
1. We prove that if rho is G_n-realizable for a sequence of graphs such that lambda_n(G_n) / lambda_1(G_n) tends to 0, then rho is described by a probability matrix that is positive-semidefinite. For random variables on domains of size |D| <= 4, this implies that rho must be an i.i.d. mix.
2. If rho is G_n-realizable for a sequence of (n,d,lambda)-graphs G_n (d-regular with all eigenvalues except for one bounded by lambda in absolute value) such that lambda(G_n) / d(G_n) tends to 0, then rho is an i.i.d. mix.
3. If rho is G_n-realizable for a sequence of directed graphs such that each of them is an arbitrary orientation of an (n,d,lambda)-graph G_n, and lambda(G_n) / d(G_n) tends to 0, then rho is an i.i.d. mix
CREPE: Learnable Prompting With CLIP Improves Visual Relationship Prediction
In this paper, we explore the potential of Vision-Language Models (VLMs),
specifically CLIP, in predicting visual object relationships, which involves
interpreting visual features from images into language-based relations. Current
state-of-the-art methods use complex graphical models that utilize language
cues and visual features to address this challenge. We hypothesize that the
strong language priors in CLIP embeddings can simplify these graphical models
paving for a simpler approach. We adopt the UVTransE relation prediction
framework, which learns the relation as a translational embedding with subject,
object, and union box embeddings from a scene. We systematically explore the
design of CLIP-based subject, object, and union-box representations within the
UVTransE framework and propose CREPE (CLIP Representation Enhanced Predicate
Estimation). CREPE utilizes text-based representations for all three bounding
boxes and introduces a novel contrastive training strategy to automatically
infer the text prompt for union-box. Our approach achieves state-of-the-art
performance in predicate estimation, mR@5 27.79, and mR@20 31.95 on the Visual
Genome benchmark, achieving a 15.3\% gain in performance over recent
state-of-the-art at mR@20. This work demonstrates CLIP's effectiveness in
object relation prediction and encourages further research on VLMs in this
challenging domain
The White-Box Adversarial Data Stream Model
We study streaming algorithms in the white-box adversarial model, where the
stream is chosen adaptively by an adversary who observes the entire internal
state of the algorithm at each time step. We show that nontrivial algorithms
are still possible. We first give a randomized algorithm for the -heavy
hitters problem that outperforms the optimal deterministic Misra-Gries
algorithm on long streams. If the white-box adversary is computationally
bounded, we use cryptographic techniques to reduce the memory of our
-heavy hitters algorithm even further and to design a number of additional
algorithms for graph, string, and linear algebra problems. The existence of
such algorithms is surprising, as the streaming algorithm does not even have a
secret key in this model, i.e., its state is entirely known to the adversary.
One algorithm we design is for estimating the number of distinct elements in a
stream with insertions and deletions achieving a multiplicative approximation
and sublinear space; such an algorithm is impossible for deterministic
algorithms.
We also give a general technique that translates any two-player deterministic
communication lower bound to a lower bound for {\it randomized} algorithms
robust to a white-box adversary. In particular, our results show that for all
, there exists a constant such that any -approximation
algorithm for moment estimation in insertion-only streams with a
white-box adversary requires space for a universe of size .
Similarly, there is a constant such that any -approximation algorithm
in an insertion-only stream for matrix rank requires space with a
white-box adversary. Our algorithmic results based on cryptography thus show a
separation between computationally bounded and unbounded adversaries.
(Abstract shortened to meet arXiv limits.)Comment: PODS 202
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