Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cs/0703095

Copula Component Analysis

Jian Ma·Zengqi Sun
View original source ↗Read source document ↗Export metadata ↓

Abstract

A framework named Copula Component Analysis (CCA) for blind source separation is proposed as a generalization of Independent Component Analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components may be dependent with certain structure which is represented by Copula. By incorporating dependency structure, much accurate estimation can be made in principle in the case that the assumption of independence is invalidated. A two phrase inference method is introduced for CCA which is based on the notion of multidimensional ICA.

Explore related subjects

cs.IRcs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jian Ma, Zengqi Sun. 2007-03-20. Copula Component Analysis. https://arxiv.org/abs/cs/0703095

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

WebArxiv: A Reproducible Benchmark for Evaluating Multimodal Web Agents on arXiv Tasks

Foundation models now enable autonomous agents to interact with real-world websites, but existing benchmarks emphasize general-purpose browsing, underrepresent research-oriented environments and scholarly discovery workflows, and often depend on live sites whose changing content and structure undermine reproducibility. arXiv provides a realistic, reproducible, hierarchically structured, information-centric testbed without privacy-sensitive interactions. We introduce WebArxiv, a static-snapshot benchmark comprising 510 time-invariant tasks, each with a unique deterministic ground truth. Its diverse, realistic scholarly tasks go beyond simple information lookup and rule following to emphasize multi-constraint paper retrieval, fine-grained content extraction, and cross-paper comparison. Evaluations of a range of foundation-model-based web agents show that WebArxiv remains challenging. Behavioral analysis reveals that agents over-rely on fixed interaction histories, causing incomplete or repetitive reasoning. We therefore equip agents with a lightweight dynamic-memory mechanism for adaptive retrieval and reasoning over relevant context. The benchmark and code are available at https://anonymous.4open.science/r/74E4423BVNW/README.md.

cs.IR↗
arXiv2026

GreekBarRetrieval: A Benchmark for Greek Statutory Retrieval

Statutory retrieval is necessary for citation-grounded legal question answering, but remains underexplored for Greek. We introduce GreekBarRetrieval, a public retrieval benchmark derived from, and complementing GreekBarBench, which did not include retrieval. The new benchmark comprises 283 bar-exam questions, each accompanied by the facts of the case it refers to, and 6,308 candidate statutory articles to retrieve from. Questions and facts are stated in everyday language, but need to be mapped to the formal terminology of statutes and their abstract legal concepts. A further complication is that not all of the case facts are relevant to each question of a case. Experimenting with three BM25 variants and nine dense retrievers, we find that vanilla dense retrieval far outperforms vanilla sparse retrieval in Recall@100. However, LLM-based query reformulation helps BM25 close that gap, while also improving dense retrieval. With a ten-round ReAct-like LLM reformulation loop that we introduce, BM25 improves further in Recall@100 and obtains the best nDCG and MAP scores of all tested retrievers. Query reformulation also outperforms pseudo-relevance feedback, sparse-dense fusion, and English translation.

cs.IR↗
arXiv2026

Parameterized Dense-Sparse Fusion for Hybrid Retrieval: Tuning a Rank-Score Mix on BEIR SciFact with Qdrant

We study a parameterized hybrid ranker that fuses a dense embedding list and a sparse lexical list. The method has a small, explicit parameter vector: a dense prior $α\in [0,1]$, a score-versus-rank mix $λ\in [0,1]$, an RRF smoothing parameter $κ> 0$, optional list-geometry coefficients that move $α$ per query, and a router margin $τ$ that can turn sparse search off. We grid-search those ranges on SciFact train (809 queries) and freeze the chosen values on SciFact test (300). The tuned rank-score mix ($α= 0.8$, $λ= 0.75$, $κ= 20$) reaches 0.753 nDCG@10 and 0.889 recall@10, outperforming dense BGE (0.742 / 0.871) and equal-weight RRF (0.707 nDCG@10) on that test split. A list-conditioned $α$ adds +0.0006 nDCG; a sparse-off router is rejected by the same train split (any $τ$ that skipped approximately 50% of queries lost nDCG). These coefficients are dataset-specific. Equal RRF with the same models does not beat dense on a nine-zip BEIR macro-average (0.479 vs. 0.519 nDCG@10). Repeating the same train-then-freeze sweep independently on all 20 indexed units beats equal RRF on 20/20 and dense on 16/20 (unit-mean nDCG@10 0.467 vs. 0.462 dense vs. 0.420 RRF). Other corpora should reuse the ranges, not a copy of the SciFact point.

cs.IR↗