Related papers: The Multivariate Covering Lemma and its Converse
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
Multi-view representation learning captures comprehensive information from multiple views of a shared context. Recent works intuitively apply contrastive learning (CL) to learn representations, regarded as a pairwise manner, which is still…
To inhibit the spread of rumorous information and its severe consequences, traditional fact checking aims at retrieving relevant evidence to verify the veracity of a given claim. Fact checking methods typically use knowledge graphs (KGs) as…
Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes -- the generalized covering radius. The generalized covering-radius hierarchy of a…
Compact and discriminative visual codebooks are preferred in many visual recognition tasks. In the literature, a number of works have taken the approach of hierarchically merging visual words of an initial large-sized codebook, but…
We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In…
We introduce the coordination principle, which states that perfect coordination, in the form of agreement on a uniformly random output, among N parties is possible only if they share a common cause. This principle is purely causal and can…
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…
Expectations of multivariate functions with missing labels occur in various fields such as transfer learning and average treatment effects. Although non-parametric estimators based on nearest-neighbour matching are frequently used in this…
This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…
We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically_mismatched_ to the source distribution), followed by optimal…
In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
A lower bound on the probability of decoding error of quantum communication channel is presented. The strong converse to the quantum channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method exept…
When language models answer open-ended problems, they implicitly make hidden decisions that shape their outputs, leaving users with uncontextualized answers rather than a working map of the problem; drawing on multiverse analysis from…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…
This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit…
Motivated by the need for real-world matching problems, this paper formulates a large class of practical choice rules, Generalized Lexicographic Choice Rules (GLCR), for institutions that consist of multiple divisions. Institutions fill…