Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1508.06885

Taxicab Correspondence Analysis of Sparse Contingency Tables

Vartan Choulakian
View original source ↗Read source document ↗Export metadata ↓

Abstract

Visualization and interpretation of contingency tables by correspondence analysis (CA), as developed by Benzecri, has a rich structure based on Euclidean geometry. However, it is a well established fact that, often CA is very sensitive to sparse contingency tables, where we caracterize sparsity as the existence of relatively high-valued counts, rare observations discussed by Rao (1995), and zero-block structure emphasized by Novak and Bar-Hen (2005) and Greenacre (2013). In this paper, we aim to emphasize the important roles played by L1 and L2 geometries. This will be done by comparing the maps obtained by CA with the maps obtained by taxicab correspondence analysis (TCA), where TCA is a robust L1 variant of correspondence analysis. If the projections of view of both maps are quite different, we refer to this phenomenon as parallax. In astronomy, parallax means the apparent change in the position of an object as seen from two different points. In our case the two different points correspond to the two different geometries, Euclidean and Taxicab. The existence of a parallax highlights the important, but hidden, role of the underlying geometry in the interpretation of the maps obtained in multivariate data analysis. We emphasize the following fact: Only by comparing CA and TCA graphical displays, we are able to reveal the phenomenon of parallax. Examples are provided.

Explore related subjects

stat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vartan Choulakian. 2017-06-02. Taxicab Correspondence Analysis of Sparse Contingency Tables. https://arxiv.org/abs/1508.06885

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

KEEP EXPLORING

Related papers

arXiv2026

Auditing Bayesian Graph Alignment: Diagnostic Comparisons and Reference Failure

Bayesian graph alignment estimates correspondence probabilities, but convergence of an alignment-score trace need not imply accurate correspondence marginals. We audit this gap on 240 new exact graph pairs from four source families, 240 larger pairs with 20-100 vertices, and a separate 60-case exact implementation check. Under an explicit edge-flip likelihood, we compare three samplers and score, marginal, indicator, categorical, and classifier-based diagnostics. Marginal disagreement improves error discrimination over score R-hat for the exact informed sampler, but its improvement for vanilla local sampling is uncertain. Assignment-based R* and short indicator panels are competitive; no diagnostic dominates across samplers and endpoints. At larger sizes, diagnostics predict subsequent marginal changes, not posterior error, and classification performance depends on the drift threshold. Disjoint-window and held-out-chain checks attenuate but preserve positive associations. Only 22 of 240 original reference sets pass an agreement screen. On forty failure-selected cases, eightfold SMC particle escalation does not resolve disagreement, whereas additional rejuvenation helps. Longer informed runs remain unstable. An elementary feasible-alignment bound demonstrates severely unrepresentative SMC and informed-chain scores in concentrated 100-vertex cases, independently of approximate reference consensus. We also exhibit common-start chains with near-zero disagreement despite exact marginal error near .967. These results support assignment-sensitive auditing while identifying limits of finite budgets, diagnostic rankings, and reference agreement as evidence of accuracy.

stat.AP↗
arXiv2026

GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation

Reliable intervention-oriented uncertainty quantification from Earth observation (EO) remains challenging when continuous treatment shifts, spatial dependence, limited support, and satellite-outcome uncertainty must be addressed simultaneously. Existing causal, conformal, and spatial approaches address parts of this problem, but their direct combination does not generally recover the appropriate interventional reference law because candidate reassignment jointly alters treatment likelihood, standardized residuals, and graph-dependent residual likelihood. This study presents GeoDose-CP, a support-aware conformal framework for localized stochastic potential outcomes under continuous or mixed continuous-atomic treatment. Its central methodological contribution is a graph-local target-orbit law that jointly represents intervention-induced treatment shift, the inverse outcome-scale Jacobian, and spatial residual dependence. The framework further provides exact weighted candidate inversion, a scalable sparse approximation with explicit discrepancy accounting, and refusal under inadequate support. Evaluation used controlled known-truth experiments, MineDoseBench, treatment-density sensitivity analysis, external conformal comparators, and a multi-mine New South Wales (NSW) study. In MineDoseBench, GeoDose-CP achieved mean selective coverage of 0.9692 across 27 configurations and a minimum local q0.05 of 0.8951; exact-sparse auditing produced nine inclusion disagreements over 2,700 targets. In the NSW study, the absence of an auditable longitudinal rehabilitation treatment rendered treatment-dependent inference nonoperational rather than forcing inference through a proxy exposure.

stat.AP↗
arXiv2026

Interpreting relative utility for probabilistic predictions

At a fixed threshold, relative utility (RU) measures the net-benefit gain of a prediction model over the better of treat-all and treat-none relative to the corresponding gain under perfect outcome classification. We illustrate that RU equal to 1 therefore represents perfect outcome classification at that fixed threshold, not perfect probabilistic prediction. However, even when every predicted probability equals the true probability, observed RU can equal 0. In a simple constant-risk setting, this occurs with probability approaching 1 as the sample size increases. Consequently, the distance from observed RU to 1 should not in general be interpreted as improvement achievable by a better prediction for binary probabilities.

stat.AP↗