Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.10360

Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices

Doudou Zhou·Tianxi Cai·Junwei Lu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Matrix completion has attracted attention in many fields, including statistics, applied mathematics, and electrical engineering. Most of the works focus on the independent sampling models under which the observed entries are sampled independently. Motivated by applications in the integration of knowledge graphs derived from multi-source biomedical data such as those from Electronic Health Records (EHR) and biomedical text, we propose the {\bf B}lock-wise {\bf O}verlapping {\bf N}oisy {\bf M}atrix {\bf I}ntegration (BONMI) to treat blockwise missingness of symmetric matrices representing relatedness between entity pairs. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption. Simulation studies show that the method performs well under a variety of configurations. In the real data analysis, the method is applied to two tasks: (i) the integrating of several point-wise mutual information matrices built by English EHR and Chinese medical text data, and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods.

Explore related subjects

stat.MLcs.LGmath.STstat.APstat.MEstat.TH

Keep this discovery

BibTeXRIS

Doudou Zhou, Tianxi Cai, Junwei Lu. 2021-05-21. Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices. https://arxiv.org/abs/2105.10360

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

KEEP EXPLORING

Related papers

arXiv2026

A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs

Feature-based explanations quantify features' influence on model predictions, but are primarily designed for scalar outputs. In many applications, however, outputs are functional or multivariate, such as time-dependent trajectories in demand forecasting. Consequently, existing approaches typically explain each output location independently, ignoring dependencies across the output components. We address this limitation by developing a unified framework for feature-based explanations of time-dependent outputs. Specifically, we generalize functional decomposition to Hilbert-valued prediction functions and extend an existing feature-based explanation framework to this setting. Our framework introduces kernel-based output representations that enable time-dependency-aware explanations at multiple levels of temporal granularity, including time-specific, time-resolved, and time-aggregated, while providing a unified view in which existing methods arise as special cases. We validate our framework on synthetic and real-world data, including intraday financial market volatility prediction and energy demand forecasting.

stat.ML↗
arXiv2026

Risk-Averse Decision Making with Multi-Level Reliability Guarantees

Many applications in engineering, including wireless broadcasting, require designs that provide performance certificates at different target outage levels. This paper studies the problem of maximizing the weighted average of such certificates in the presence of uncertainty about the true system state. The problem is shown to be equivalent to an optimization over nested prediction sets, connecting to the literature on conformal prediction and extending prior art on single-level risk-averse decision making. Furthermore, we derive a dual formulation that decouples optimization across input values. Numerical experiments on a diversity-based wireless transmission system illustrate the cost of enforcing multi-level certificates with a single shared policy and trace the Pareto trade-off between multiple reliability levels.

stat.ML↗
arXiv2026

A distribution-free certification framework for trustworthy crash-severity prediction

Crash-severity models inform screening, dispatch and site prioritization, yet are deployed without a finite-sample statement of what one prediction means. Off-the-shelf guarantees fail here, because the features that make crash severity distinctive defeat them: the KABCO outcome is ordinal, the recorded label is a field assessment agreeing with medical severity about half the time, erring in a structured way, and deployment crosses jurisdictions and years calibration never saw. We develop a certification layer that wraps any severity model unmodified, with distribution-free guarantees using this structure: contiguous ordinal sets that read as "B or worse"; per-class validity for any pre-declared partition, with an oracle efficiency characterization; transfer of coverage to unobserved true severity through a declared reporting band, with a worst-case sharpness result; a one-sided certificate under deployment shift; and severity-weighted risk control. The guarantees compose with an attributable slack budget. The same analysis bounds what certification can achieve. A certified set's informativeness is governed by a functional of the true law that no base model can evade and that cannot be lower-bounded distribution-free; given a declared misreporting channel identified from record-linkage data, a nonvacuous lower bound on that floor becomes computable. On 5.2 million Texas records across seven base models spanning four decades, the layer attaches identical validity and certifies, on the vulnerable road users, a model-independent floor on set width that no base model beats, separating it from a remainder that stays bounded but distribution-free unidentifiable. The framework is released as an open-source package with theorem-level tests.

stat.ML↗