arXiv subjects

Jiangying Luo

Publications and source records attributed to Jiangying Luo.

3 recordsLinked to original sources

arXiv2026

Common Geodesics Do Not Guarantee Fisher Consistency of the Structured SVM: Minimal Counterexamples and a Tree-Metric Classification

A known necessary condition for Fisher consistency of the structured support vector machine requires the task loss to be a metric for which every output triple has a common geodesic point. We show that this condition is not sufficient for the canonical coordinate-wise argmax decoder. A four-output unit star admits an exactly optimal score vector whose maximizers are all strictly non-Bayes, and four outputs are minimal among metrics satisfying the condition. We then completely classify positively weighted tree metrics whose vertex set is the output space: argmax consistency holds if and only if the tree is a path. The failure on branching trees is confined to boundary distributions; every tree retains the argmax property at every full-support distribution. Among metrics satisfying the common-geodesic condition, five outputs are necessary and sufficient for a full-support counterexample; $K_{2,3}$ is the smallest member of an infinite $K_{m,n}$ family. We additionally give a full-support counterexample for the three-dimensional Hamming cube. All optimality claims have exact primal-dual certificates. The counterexamples expose a concrete decoder gap: in this polyhedral setting, an embedding can guarantee the existence of a calibrated link without validating a prescribed argmax link on every surrogate-risk minimizer.

cs.LG↗

arXiv2026

Rank-Three Projections and Minimal Multiplicity Bipartitions of Path Complements

For a graph $G$ admitting a real symmetric realization with exactly two distinct eigenvalues, $MB(G)$ is the minimum, over all such realizations, of the smaller of the two eigenvalue multiplicities. Adm, Fallat, Meagher, Nasserasr, Plosker, and Yang asked for this parameter for the complement of a path on at least eight vertices. We answer their question completely by proving $$ MB(\overline{P_n})=3 \qquad (n\ge 6). $$ In particular, this resolves the previously unresolved orders $n\ge 9$ divisible by three. The proof is exact and constructive. We exhibit six vectors in $\mathbb{R}^3$ whose mutual inner products vanish exactly for consecutive indices, whose rank-one outer products form a basis of $\mathbb{S}^3$, and which admit a strictly positive Parseval scaling. An elementary absorption lemma then permits any finite faithful orthogonal extension of this vector chain to be added with small positive weights while the six original weights are corrected to retain the Parseval identity. The resulting Gram matrix is a rank-three orthogonal projection in $\mathcal{S}(\overline{P_n})$. A local two-dimensional orthogonality obstruction gives the matching lower bound. For completeness, we include self-contained proofs of the exceptional small orders: $MB(\overline{P_3})=1$, whereas $q(\overline{P_4})=4$ and $q(\overline{P_5})=3$.

cs.DM↗

arXiv2024

Self-supervised inter-intra period-aware ECG representation learning for detecting atrial fibrillation

Atrial fibrillation is a commonly encountered clinical arrhythmia associated with stroke and increased mortality. Since professional medical knowledge is required for annotation, exploiting a large corpus of ECGs to develop accurate supervised learning-based atrial fibrillation algorithms remains challenging. Self-supervised learning (SSL) is a promising recipe for generalized ECG representation learning, eliminating the dependence on expensive labeling. However, without well-designed incorporations of knowledge related to atrial fibrillation, existing SSL approaches typically suffer from unsatisfactory capture of robust ECG representations. In this paper, we propose an inter-intra period-aware ECG representation learning approach. Considering ECGs of atrial fibrillation patients exhibit the irregularity in RR intervals and the absence of P-waves, we develop specific pre-training tasks for interperiod and intraperiod representations, aiming to learn the single-period stable morphology representation while retaining crucial interperiod features. After further fine-tuning, our approach demonstrates remarkable AUC performances on the BTCH dataset, \textit{i.e.}, 0.953/0.996 for paroxysmal/persistent atrial fibrillation detection. On commonly used benchmarks of CinC2017 and CPSC2021, the generalization capability and effectiveness of our methodology are substantiated with competitive results.

q-bio.QM↗