### 符号表

• $$S=\{\mathbf{z}_i\}_{i=1}^n=\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n$$
• Dataset
• $$\mathcal{H}$$
• function space
• $$f_{\mathbf{\theta}}:\mathcal{X}\to \mathcal{Y}$$
• hypothesis function
• $$L_{S}(\mathbf{\theta}), L_{n}(\mathbf{\theta}), R_{n}(\mathbf{\theta}), R_{S}(\mathbf{\theta})$$
• empirical risk or training loss
• $$f(\mathbf{x};\mathbf{\theta})=\sum_{j=1}^{m} a_j \sigma (\mathbf{w}_j\cdot \mathbf{x} + b_j)$$
• two-layer neural network
• $${\rm Rad}_{n} (\mathcal{H})$$
• GD
• SGD
• $$B$$
• a batch set
• $$|B|$$
• batch size
• $$\eta$$
• learning rate
• $$\mathbf{\xi}$$
• continuous frequency

### 专家评语

The document provides comprehensive, clear mathematical notations that commonly used in machine learning. These consistent definitions are easily accessible for beginners and facilitate the communications of researchers from different backgrounds, which are important for the development of this interdisciplinary subject.
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Machine learning has developed as an interdisciplinary field and impacted many other domains significantly. This has attracted researchers from different domains to involve the development of machine learning, including those from statistics, applied math, physics, computer science, electrical engineering, etc. This definitely raise the requirement to communicate with each other smoothly, and particularly, a consistent notation system is in demand. This proposal is an important starting step towards this goal. Thanks for the authors’ efforts! Indeed, this notation systems requires researchers from all the related fields to contribute and provide suggestions.
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### 符号表

symbolmeaningLATEXsimplied
xinput\bm{x}\vx
youtput, label\bm{y}\vy
dinput dimensiond
dooutput dimension d_{\rm o}d_{\rm o}
nnumber of samplesn
Xinstances domain (a set)\mathcal{X}\fX
Ylabels domain (a set)\mathcal{Y}\fY
Z= X × Y example domain\mathcal{Z}\fZ
Hhypothesis space (a set)\mathcal{H}\fH
θa set of parameters\bm{\theta}\vtheta
fθ : X → Yhypothesis function\f_{\bm{\theta}}f_{\vtheta}
f or f ∗ : X → Ytarget functionf,f^*
ℓ : H × Z → R+loss function\ell
Ddistribution of Z\mathcal{D}\fD
S = {zi}ni=1= {(xi, yi)}ni=1 sample set
LS(θ), Ln(θ),empirical risk or training loss
Rn(θ), RS(θ)empirical risk or training loss
LD(θ), RD(θ)population risk or expected loss
σ : R → R+activation function\sigma
wjinput weight\bm{w}_j\vw_j
ajoutput weighta_j
bjbias termb_j
f∑θ(x) or f(x; θ)neural networkf_{\bm{\theta}}f_{\vtheta}
∑mj=1 ajσ(wj · x + bj )two-layer neural network
VCdim(H)VC-dimension of H