CSMD: A Multi-Domain Acronym Overview

• CSMD is a polysemous acronym whose meaning shifts by discipline, defined in contexts ranging from cosmic stellar-mass density in FRB studies to curated datasets in financial analysis.
• Each interpretation employs specialized methodologies, including polynomial fitting for redshift evolution, LLM-enhanced factor extraction in stock analysis, and non-Euclidean prox techniques in stochastic optimization.
• The diverse uses—from quark-level molecular dynamics to online cost-sensitive medical diagnosis—highlight the importance of contextual clues for accurate acronym disambiguation.

CSMD is a polysemous acronym in contemporary research literature. In current arXiv usage it denotes several unrelated technical entities: cosmic stellar-mass density in fast radio burst population modeling, Curated Multimodal Dataset for Chinese Stock Analysis, Composite Stochastic Mirror Descent, Color-Spin Molecular Dynamics, and Cost-Sensitive Medical Diagnosis (Hashimoto et al., 2020, Liu et al., 3 Nov 2025, Ilandarideva et al., 2022, Yasutake et al., 7 Apr 2026, Verma et al., 2019). The term therefore has no discipline-independent meaning; its interpretation is fixed by the surrounding domain, mathematical formalism, and application context.

1. Scope of the acronym

The major current uses of CSMD span observational cosmology, multimodal financial machine learning, stochastic convex optimization, quark-level neutron-star matter modeling, and unsupervised online medical decision-making. These usages are not historically or methodologically connected. In one case CSMD is a cosmic population tracer; in another it is a curated benchmark dataset; in another it is a composite non-Euclidean stochastic algorithm; in another it is a many-body dynamical framework with internal color and spin; and in another it is a bandit-style feature-selection problem.

This cross-domain reuse makes acronym disambiguation nontrivial. In practice, the intended meaning is usually identifiable from the neighboring vocabulary: FRB luminosity functions and redshift evolution indicate cosmic stellar-mass density; Baostock, STCN, or LightQuant indicate the Chinese stock-analysis dataset; prox mappings, Bregman divergences, and sparse GLR indicate Composite Stochastic Mirror Descent; quark clustering and beta equilibrium indicate Color-Spin Molecular Dynamics; and Weak Dominance, Thompson Sampling, or medical tests indicate Cost-Sensitive Medical Diagnosis.

2. CSMD as cosmic stellar-mass density

In FRB population modeling, CSMD stands for cosmic stellar-mass density. It is used as one of two candidate prescriptions for the redshift evolution of the FRB luminosity function, the other being CSFRD. The empirical luminosity function at a reference redshift is rescaled by a factor $f(z)$, with the CSMD case taking $f(z)$ to follow the observed cosmic stellar-mass density evolution. For non-repeating FRBs and repeating FRBs, respectively, the paper writes

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$

and

$$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$

For the CSMD case, $f(z)$ is the best-fit 8th-degree polynomial to the observed CSMD from López et al. (2018): $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$ The detectable counts are then obtained by integrating the redshift-dependent luminosity function over the survey volume, with

$$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$

and a cumulative count

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$

The astrophysical motivation is that CSMD evolution is treated as the plausible case if FRBs come from old stellar populations with long delay times, such as white dwarfs, neutron stars, and black holes, whereas CSFRD evolution is favored for young stellar populations or short-delay progenitors such as supernova remnants, magnetars, and pulsars. The paper states that non-repeating FRBs are better matched by CSMD, while repeating FRBs are better matched by CSFRD. Under the CSMD assumption for non-repeaters, the SKA detection rates are predicted to be $\sim10^{4}$ sky$f(z)$0 day$f(z)$1 at $f(z)$2, $f(z)$3 sky$f(z)$4 day$f(z)$5 at $f(z)$6, and $f(z)$7 sky$f(z)$8 day$f(z)$9 at $$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$0. Switching from CSMD to CSFRD can change the predicted rates by about one order of magnitude, and the paper emphasizes that this effect is much larger than the effects of free-free absorption, Galactic coordinates, and scattering. The association of several known non-repeating FRB hosts—FRB 180924, FRB 181112, and FRB 190523—with massive or moderately massive galaxies is presented as support for a CSMD-tracing population (Hashimoto et al., 2020).

3. CSMD as Curated Multimodal Dataset for Chinese Stock Analysis

In quantitative finance, CSMD stands for Curated Multimodal Dataset for Chinese Stock Analysis. It was introduced to address three identified deficiencies in existing resources: country/language mismatch, noisy text, and high research overhead. The dataset combines price/market data from Baostock with financial news text from Securities Times (STCN), and it is designed to align news and price data temporally. Two benchmark variants are defined: CSMD 300, based on the constituents of CSI 300, and CSMD 50, based on the constituents of SSE 50. Construction proceeds in three stages: news collection through a scalable automated pipeline, LLM-enhanced factor extraction using LLMs with sequential/domain prompts, and data quality validation along five aspects—denoising, financial sentiment expression, text density, human readability, and LLM readability. Validation combines manual review by 5 financial-domain experts with automatic assessment using MiniLM-L6-v2 and GPT-4 (Liu et al., 3 Nov 2025).

Dataset	Stocks	Time Range
CSMD 300	300	2021–2024
CSMD 50	50	2021–2024

The downstream tasks are stock trend prediction and backtesting. Prediction is evaluated by ACC and MCC; backtesting is evaluated by ARR, SR, MDD, and CR. The accompanying framework, LightQuant, is a modular three-layer framework with a data layer, model layer, and evaluation layer. It supports data processing, feature engineering, model training, evaluation, backtesting, and visualization, and is positioned as a simplified alternative to heavier quantitative platforms. The experimental suite includes single-modal models—LSTM, BiLSTM, ALSTM, Adv-LSTM, SCINet, and DTML—and multimodal models—StockNet, HAN, and PEN. On CSMD 300, StockNet achieves 55.47 ACC and 0.0916 MCC, HAN achieves 55.00 ACC and 0.0972 MCC, and DTML achieves 54.13 ACC and 0.1478 MCC; on CSMD 50, StockNet achieves 55.11 ACC, HAN achieves 54.69 ACC and 0.1002 MCC, and DTML achieves 54.12 ACC and 0.0972 MCC. In backtesting on CSMD 50, StockNet gives ARR = 0.1301 and CR = 3.0182, ALSTM gives SR = 0.8192, and HAN gives MDD = 0.0149. The reported comparison with CMIN-CN indicates that CSMD improves trend prediction across most models and supports meaningful trading outcomes under risk-aware evaluation.

4. CSMD as Composite Stochastic Mirror Descent

In stochastic optimization, CSMD denotes Composite Stochastic Mirror Descent, a non-Euclidean stochastic approximation method for large-scale sparse recovery. The generic problem is

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$1

with a composite penalized formulation

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$2

The principal statistical application is sparse generalized linear regression, where one seeks an unknown sparse vector $$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$3 from observations

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$4

and the stochastic loss is written as

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$5

The analysis assumes smoothness of $$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$6, quadratic minoration or curvature, sub-Gaussian stochastic gradient noise at the optimum, and an RSC-type condition appropriate to sparsity. The framework is not limited to coordinate sparsity; it also covers group sparsity and low-rank matrix recovery via appropriate norms and projectors (Ilandarideva et al., 2022).

The algorithm is built on a distance-generating function $$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$7 and the associated Bregman divergence on a local set $$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$8. With

$$\log\Phi_{\rm NR}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm NR}^{\rm emp}(z=0.16)+\log \left[ \frac{f(z)}{f(z=0.16)} \right]$$9

$$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$0

and

$$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$1

the CSMD recursion with $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$2 is

$$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$3

and the output after $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$4 steps is a weighted average. For sparse recovery in $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$5 geometry, the method uses

$$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$6

which yields $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$7.

The distinctive features of CSMD are its explicit handling of the nonsmooth penalty inside the prox step, its non-Euclidean geometry, its sparse-friendly mirror map, and its embedding in a multistage routine with shrinking neighborhoods and stage-specific penalties. The single-stage analysis gives high-probability bounds on $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$8, and the multistage CSMD-SR scheme exhibits a preliminary linear phase followed by an asymptotic sublinear phase. In sparse GLR with bounded regressors and covariance $$\log\Phi_{\rm R}^{\rm emp}(z, \log L_{\nu})=\log\Phi_{\rm R}^{\rm emp}(z=0.17)+\log \left[ \frac{f(z)}{f(z=0.17)} \right].$$9, the paper derives

$f(z)$0

and interprets the norm distance from $f(z)$1 as the radius of a confidence ball. The reported numerical study compares CSMD-SR with vanilla non-Euclidean SMD, p-norm RDA, a prior multistage SMD method, and Euclidean SGD, and identifies faster convergence and better approach to the noise-dominated regime for the multistage composite method.

5. CSMD as Color-Spin Molecular Dynamics

In dense-matter theory, CSMD means Color-Spin Molecular Dynamics. It is a molecular-dynamics framework for quark matter in which each quark is represented by a Gaussian wave packet whose center-of-mass position, center-of-mass momentum, and internal color and spin states are dynamical variables. The many-body wave function is taken as a direct product of single-quark packets,

$f(z)$2

with $f(z)$3. The paper emphasizes three advances over earlier MD work: inclusion of strangeness, time evolution of internal spin degrees of freedom, and consistent treatment of spin-dependent interactions. The system studied is dense neutron-star matter at the quark level, containing $f(z)$4, $f(z)$5, and $f(z)$6 quarks plus electrons under charge neutrality and beta equilibrium (Yasutake et al., 7 Apr 2026).

The Hamiltonian is

$f(z)$7

Its components are relativistic kinetic energy, a color interaction $f(z)$8, a color-spin interaction $f(z)$9, a color-independent quark-meson exchange interaction $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$0, and a phenomenological Pauli repulsion. Time evolution is obtained through Euler–Lagrange equations for

$\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$1

followed by frictional cooling to the ground state. The EOS is built by minimizing the energy per baryon at each baryon density $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$2 under charge neutrality and beta equilibrium, allowing the flavor conversion

$\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$3

For beta-equilibrated matter with strangeness, the paper uses an interpolation formula

$\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$4

to capture the onset of strangeness.

The main physical conclusions concern clustering and flavor-sector interactions. Using the diagnostic criterion

$\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$5

the stable neutron-star branch shows no isolated quark-like configurations within the present CSMD framework and the adopted clustering criterion. Instead, color-magnetic interactions favor the self-consistent formation of multi-quark clusters, and the cluster-size distribution is concentrated at

$\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$6

corresponding to integer baryon numbers. When $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$7 is turned off, isolated $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$8 quark-like configurations appear at the highest densities and the $\begin{split} f(z)&=8.156+5.906\times10^{-2}z-7.111\times10^{-2}z^{2}+4.034\times10^{-2}z^{3} \ &\quad-1.256\times10^{-2}z^{4}+2.209\times10^{-3}z^{5}-2.216\times10^{-4}z^{6} \ &\quad+1.179\times10^{-5}z^{7}-2.585\times10^{-7}z^{8}. \end{split}$9 pattern breaks down, indicating that color-magnetic interactions are the key driver of clustering. The strange-light interaction is modeled through the $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$0 channel with sampled values

$$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$1

and the paper identifies

$$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$2

as the best-performing sampled case, while stressing that this is not a unique best-fit. All sampled models satisfy

$$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$3

A plausible implication is that future radius measurements could help constrain strange-light interactions and the density at which strangeness appears.

6. CSMD as Cost-Sensitive Medical Diagnosis

In online learning and medical decision-making, CSMD stands for Cost-Sensitive Medical Diagnosis. The setting models diagnosis as an online feature selection problem in which each medical test yields a feature, tests have nonnegative costs, and the true patient state is unknown to the learner. A problem instance is $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$4, where $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$5 is an unknown distribution over the binary vector

$$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$6

and $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$7 is the vector of feature or test costs. In round $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$8, the environment generates $$N=\int \Phi^{\rm emp}(z, \log L_{\nu})\, V_{\rm survey}(z_{1},z_{2},\log L_{\nu})\, d\log L_{\nu},$$9, the learner selects an arm $$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$0, observes $$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$1, and incurs loss

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$2

With $$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$3 WLOG, the expected loss of arm $$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$4 is

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$5

and the optimal arm is

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$6

The objective is to minimize the pseudo-regret

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$7

Learning without labels is made possible by the Weak Dominance (WD) property. If $$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$8 satisfies WD, then

$$V_{\rm survey}(z_{1},z_{2},\log L_{\nu})=V_{\rm max,4\pi}\,\Omega_{\rm sky}\, t_{\rm obs}/(1+z),$$9

The paper states that the set of instances satisfying WD is maximally learnable. In the cascade version, the optimal arm must lie in two sets,

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$0

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$1

which are estimated from pairwise disagreement probabilities. The proposed cascade algorithms are CSMD-TS, which maintains Beta posteriors over pairwise disagreements and samples

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$2

and CSMD-kl, which constructs a KL-UCB index

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$3

The combinatorial extension allows any non-empty subset of the $$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$4 features, giving

$$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$5

subset-arms, and introduces CSMD-ESCB and CSMD-CTS.

The empirical evaluation uses Heart Disease (Cleveland) and PIMA Indians Diabetes, with feature groups mapped to medical test bundles and classifier outputs generated by logistic regression. Because the datasets are small, the authors use random oversampling to enlarge them to 10,000 samples. The experiments report cumulative regret with 95% confidence intervals over 100 repetitions. The main findings are that regret is sublinear when WD holds, linear when WD does not hold, the WD margin $$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$6 controls difficulty, and Thompson Sampling variants consistently outperform UCB-based variants. In the combinatorial setting, CSMD-CTS outperforms both kl-UCB and UCB1 approaches (Verma et al., 2019).

7. Related nomenclature and acronym disambiguation

A recurring source of confusion is proximity to other acronyms in neighboring literatures. Class-Specific Distribution Alignment is abbreviated CSDA, not CSMD. It is a semi-supervised medical image classification framework based on self-training, class-dependent marginal prediction alignment, EMA-based statistics, adaptive temperature scaling, and a Variable Condition Queue (VCQ); its domain and formalism are distinct from all CSMD usages listed above (Huang et al., 2023). Likewise, conditional multidimensional scaling is presented as conditional MDS / CMD scale, not as CSMD. That method estimates low-dimensional coordinates from pairwise dissimilarities in the presence of incomplete conditioning variables, jointly updating $$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$7, $$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$8, and the missing block $$N(\geq z)=\int_{z}^{z_{\rm lim}} \frac{N}{\Delta z}\, dz.$$9 by a majorization-minimization or SMACOF-style algorithm, with an equal-weight implementation of asymptotic cost $\sim10^{4}$0 (Bui, 20 Sep 2025).

This suggests that acronym-only retrieval is intrinsically unstable in technical corpora. For researchers, the operative unit of meaning is not the string “CSMD” in isolation but the surrounding disciplinary signature: redshift-evolution fits and FRB host galaxies, Chinese stock benchmarks and backtesting metrics, Bregman-proximal sparse recovery, quark-cluster EOS modeling, or label-free medical test selection.