去美国吧
科大金融多
讲师没意思
女性也要发展前景
港校不要港土博士

Note

Note

bash command

shopt -s dotglob 让通配符(glob)能匹配.开头的文件

latex bug?

setlength 经常失效，以后研究一下

incremental QR/SVD

  1. 选到同一线性空间的基比较失败
  2. 正交化比较耗费时间

Annual report

Annual report

Dear WU Zihan (56574137),

 I am writing to remind you that you are required to submit a qualifying/annual progress report on 15-Aug-2023.

Please note the following in preparation of your report:

  1. The report shall include a survey of the relevant literature, an identification of a specific research topic, the research methodology and a discussion on the possible outcome.
  2. It should be typed and written in English.
  3. The report shall be covered by a cover sheet (downloadable from AIMS). Please perform the following steps to obtain the cover sheet for your report:
  4. Log onto CityU “e-Portal”
  5. Select AIMS
  6. Click on “Student Record” > “My Study Details (for Research Degree Programmes)”
  7. Click on “Cover Sheet of Qualifying/Annual Progress Report” at the bottom of the page
  8. Select Report Type and Click Go
  9. Select the “Submission Due Date” of the current year
  10. Follow the instruction to download and print the cover sheet
  11. Follow the instruction to download and print the blank assessment form (SGS35/SGS35A for Qualifying Report, SGS36/SGS36A for Annual Progress Report)*

* SGS35/SGS36 for regular PhD/MPhil students; SGS35A/SGS36A for Joint PhD students under the Mainland Collaboration Schemes.

Please submit (i) the cover sheet, (ii) the assessment form with Section A (and E) completed, and (iii) your qualifying/annual progress report with relevant supporting materials (including the list of publication in Planner) to your supervisor by the due date for assessment arrangements. Students who fail to submit the qualifying/annual progress reportby the stipulated date without the prior approval of the Department/School should note the following:

  1. Their stipend or studentship, if applicable, will be suspended from the following month;
  2. A reminder will be issued to the students stipulating a final reportsubmission deadline. Should the students fail to submit the report by the final deadline, their study may be suspended or terminated.

Students with recommendation other than to continue their PhD/MPhil study (and studentship if applicable) will receive notification from SGS regarding the special arrangement.

If you have any queries concerning the above, please contact the following office:

Joint PhD Programme (Suzhou):                (86) 512-87161382, yanqu2@cityu.edu.cn

Joint PhD Programme (Shenzhen):           (86) 755-86581506, zhihliu@cityu.edu.cn

Regular MPhil/PhD Programme:                (852) 3442-9076, sg@cityu.edu.hk

Regards,

Chow Yei Ching School of Graduate Studies

cc            Supervisor

Notes for supervisors:

The supervisor is invited to distribute the qualifying/annual progress reports to the Qualifying Panel members for assessment, coordinate the assessment, obtain feedback from the student and return the completed assessment form to Chow Yei Ching School of Graduate Studies, via Department Head/School Dean and C/SGSC Chair (if applicable), by 15-Sep-2023. Supervisors could check the outstanding report(s) of their supervised students via AIMS > My Courses > Research Degree Student Enquiry > Student List.

Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

Acts

Acts

  • 87.3 (1) This section applies to applications for visas or other documents made under subsections 11(1) and (1.01), other than those made by persons referred to in subsection 99(2), to sponsorship applications made under subsection 13(1), to applications for permanent resident status under subsection 21(1) or temporary resident status under subsection 22(1) made by foreign nationals in Canada, to applications for work or study permits and to requests under subsection 25(1) made by foreign nationals outside Canada.
    这个说明本法适用(## Immigration and Refugee Protection Act)

    • 30 (1) A foreign national may not work or study in Canada unless authorized to do so under this Act.
      30（1）外国国民不得在加拿大工作或学习，除非根据本法获得授权。
      Marginal note:Authorization 授权
      (1.1) An officer may, on application, authorize a foreign national to work or study in Canada if the foreign national meets the conditions set out in the regulations.
      (1.1)如果外国国民符合条例规定的条件，官员可根据申请批准该外国国民在加拿大工作或学习。
    • (1.2) Despite subsection (1.1), the officer shall refuse to authorize the foreign national to work in Canada if, in the officer’s opinion, public policy considerations that are specified in the instructions given by the Minister justify such a refusal.
      (1.2)尽管有第（1.1）款的规定，如果官员认为部长在指示中具体说明的公共政策考虑是拒绝批准外国国民在加拿大工作的理由，则该官员应拒绝批准该外国国民在加拿大工作。

  • Marginal note:Concurrence of second officer
    二副同意

    (1.3) In applying subsection (1.2), any refusal to give authorization to work in Canada requires the concurrence of a second officer.
    (1.3)在适用第（1.2）款时，任何拒绝给予在加拿大工作的行为都需要得到一名二副的同意。

拒绝行为限制

  • 默认拒绝的规定：
    [24] Mandamus is a discretionary, equitable remedy. The parties agree on the legal test for mandamus, as set out in Apotex Inc. v. Canada (Attorney General), [1994] 1 F.C. 742 (C.a.), at pages 766–769, affd [1994] 3 S.C.R. 1100, which has been applied in the immigration context (see for example Conille v. Canada (Minister of Citizenship and Immigration), [1999] 2 F.C. 33 (T.d.); Vaziri v. Canada (Minister of Citizenship and Immigration), 2006 FC 1159, 52 admin. L.R. (4th) 118): 1. There must be a public legal duty to act … 2. The duty must be owed to the applicant … 3. There is a clear right to performance of that duty, in particular: (a) the applicant has satisfied all conditions precedent giving rise to the duty; … (b) there was (i) a prior demand for performance of the duty; (ii) a reasonable time to comply with the demand unless refused outright; and (iii) a subsequent refusal which can be either expressed or implied, e.g. unreasonable delay; … 4. Where the duty sought to be enforced is discretionary, the following rules apply: (a) in exercising a discretion, the decision-maker must not act in a manner which can be characterized as “unfair”, “oppressive” or demonstrate “flagrant impropriety” or “bad faith”; (b) mandamus is unavailable if the decision-maker’s discretion is characterized as being “unqualified”, “absolute”, “permissive” or “unfettered”; (c) in the exercise of a “fettered” discretion, the decisionmaker must act upon “relevant”, as opposed to “irrelevant”, considerations; (d) mandamus is unavailable to compel the exercise of a “fettered discretion” in a particular way; and (e) mandamus is only available when the decision-maker’s discretion is “spent”; i.e., the applicant has a vested right to the performance of the duty. … 5. no other adequate remedy is available to the applicant… 6. The order sought will be of some practical value or effect… 7. The Court in the exercise of its discretion finds no equitable bar to the relief sought… 8. On a “balance of convenience” an order in the nature of mandamus should (or should not) issue. [Citations omitted; emphasis in original.]

  • Mandamus（命令令状）

Mandamus是一种自由裁量的、公平的救济方式。双方都同意Mandamus的法律测试，即：

  1. 必须有一项公共法律义务去行动。
  2. 义务必须是欠给申请人的。
  3. 必须有明确的权利来执行该义务，特别是：
    • (a) 申请人已经满足了产生义务的所有先决条件；
    • (b) 必须有：
      • (i) 对义务的履行提出先前的要求；
      • (ii) 除非直接拒绝，否则有合理的时间来遵守要求；
      • (iii) 可以是明示或暗示的后续拒绝，例如不合理的延迟。
  4. 如果要执行的义务是自由裁量的，那么应用以下规则：
    • (a) 在行使自由裁量权时，决策者不能以可以被描述为“不公平”、“压迫性”的方式行事，也不能表现出“明显的不当行为”或“恶意”；
    • (b) 如果决策者的自由裁量权被描述为“无条件的”、“绝对的”、“允许的”或“无限制的”，则mandamus不可用；
    • (c) 在行使“有限制的”自由裁量权时，决策者必须基于“相关的”而非“无关的”考虑因素行事；
    • (d) mandamus不能用来强制以特定方式行使“有限制的”自由裁量权；
    • (e) 只有当决策者的自由裁量权已“用尽”时，mandamus才可用；即，申请人有权利执行该义务。
  5. 对申请人来说，没有其他充分的救济方法。
  6. 所寻求的命令将具有一些实际的价值或效果。
  7. 法院在行使其自由裁量权时，没有找到阻止寻求救济的公平障碍。
  8. 在“方便的平衡”上，应该（或不应该）发布类似于mandamus的命令。
  • 部长的职权：Judith Snider法官在上述案例Vaziri中的决定确认了部长确实拥有这一一般行政职权。

BGP signed messages

BGP signed messages

每个loyal lieutenant是通过两轮信息传递就能确定commander是不是traitor, 他们收到了所有的”commander 发给每个loyal lieutenant的信息”, 于是可以做出同样的选择。

CUR Decomposition

CUR Decomposition

$$
A \simeq C U R \
C = A(:,q) \
R = A(p,:) \
U = C^\dagger A R^\dagger \
p \text{ is a subset of } {1, \dots, m} \
q \text{ is a subset of } {1, \dots, n} \
$$

$$
A \in \mathbb{R}^{m \times n} \
A = VSW^\top \
S \in \mathbb{R}^{k \times k} \
$$

DEIM then is used to find $p$ and $q$ from $V$ and $W$.

$p$

1
cellfun(@(x) x.group, frames)

@ is a handler, which represent x temporarily. Just like a pronoun.

Construction of Ito Intergration

Construction of Ito Intergration

1. Idea

Just like the construction of Lebesgue integral, we first define the integral for elementary (simple functions), then extend it to the class of where the integral is well-defined.

Elementary Functions

For a given partition $P = {t_0, t_1, \cdots, t_n}$ of $[0, T]$, we define the elementary function $\phi$ as

$$
\phi = \sum_{i=0}^{n-1} e_i(\omega) \chi_{[t_{i}, t_{i+1})}(\omega)
$$

where $e_i$ is a $\mathcal{F}{t{i}}$-measurable random variable.

2. Ito Isometry

For $\phi$ is an elementary function, we define the Ito integral of $\phi$ as

$$
\int_{S}^{T} \phi(t, \omega) \mathrm{d}B_t = \sum_{i=0}^{n-1} e_i(\omega) (B_{t_{i+1}} - B_{t_{i}})
$$

The Ito isometry states that

$$
\mathbb{E} \left[ \left( \int_{S}^{T} \phi(t, \omega) \mathrm{d}B_t \right)^2 \right] = \mathbb{E} \left[ \int_{S}^{T} \phi^2(t, \omega) \mathrm{d}t \right]
$$

3. Ito Integral

$\mathcal{V}$

Denote the class we want to define the integral as $\mathcal{V}$. Let $\mathcal{V} = \mathcal{V}(S, T)$ be the class of all functions $f(t, \omega): [0, \infty) \times \Omega \rightarrow \mathbb{R}$ such that

  1. $f(t, \omega)$ is $\mathcal{B} \times \mathcal{F}$-measurable, where $\mathcal{B}$ is the Borel $\sigma$-algebra on $[0, \infty)$.

  2. $f(t, \omega): \omega \mapsto f(t, \omega)$ is $\mathcal{F}_t$-measurable for each $t \geq 0$.

  3. $\mathbb{E} \left[ \int_{0}^{\infty} f^2(t, \omega) \mathrm{d}t \right] < \infty$.

Step 1

Handle the bounded and continuous case.

Bounded and continuous functions in $\mathcal{V}$ can be approximated by elementary functions.

Lemma 1. If $g \in \mathcal{V}$ is bounded and continuous, then there exists a sequence of elementary functions $\phi_n \in \mathcal{V}$ such that

$$
\mathbb{E} \left[ \int_{S}^{T} (g(t, \omega) - \phi_n(t, \omega))^2 \mathrm{d}t \right] \rightarrow 0
$$

as $n \rightarrow \infty$.

Here bounded convergence theorem is used.

Theorem 1. (Bounded Convergence Theorem) Let $f_n$ be a sequence of bounded measurable functions that are supported on a set $E$ of finite measure. If $f_n \rightarrow f$ pointwise a.e. on $E$, then

$$
\lim_{n \rightarrow \infty} \int_{E} |f_n - f| \mathrm{d}\mu = 0
$$
Consequently,
$$
\lim_{n \rightarrow \infty} \int_{E} f_n \mathrm{d}\mu = \int_{E} f d\mu
$$

Proof of Lemma 1.

Define $\phi_n$ as

$$
\phi_n(t, \omega) = \sum_{i=0}^{n-1} g(t_i, \omega) \chi_{[t_{i}, t_{i+1})}(t)
$$
thus $\phi_n$ is an elementary function.

$$
\int_S^T (g-\phi_n)^2 \mathrm{d}t \rightarrow 0， \text{as } n \rightarrow \infty \tag{1}
$$
since $g$ is continuous and $[S, T]$ is compact.

Proof of (1)

Given $\omega$, $\forall \epsilon > 0$, $\exists \delta > 0$ such that
$\forall t, t’ \in [S, T]$ with $|t - t’| < \delta$, we have $|g(t, \omega) - g(t’, \omega)| < \sqrt{\frac{\epsilon}{T-S}}$. Choose $n$ such that $\frac{1}{n} < \frac{\delta}{2}$, then
$$
|g(t, \omega) - \phi_n(t, \omega)|^2 = |g(t, \omega) - g(t_i, \omega)|^2 < \frac{\epsilon}{T-S}
$$
since $|t - t_i| < \frac{2}{n} < \delta$.

Thus we have
$$
\int_S^T (g-\phi_n)^2 \mathrm{d}t < \frac{\epsilon}{T-S} \int_S^T \mathrm{d}t = \epsilon
$$

Denote $I_n(\omega) = \int_S^T (g-\phi_n)^2 \mathrm{d}t$, Eq.(1) suggests that $I_n(\omega) \rightarrow 0$ pointwisely respect to $\omega$.

Here we just need to verify that $I_n(\omega)$ is bounded and measurable, then we can apply the bounded convergence theorem.

  • Boundedness: $I_n(\omega) \leq \int_S^T g^2 \mathrm{d}t < M^2 (T-S)$, where $M$ is the bound of $g$.
  • Measurability: $I_n(\omega)$ is measurable since $g$ is measurable according to Fubini’s theorem.

Step 2

Handle the bounded (but not necessarily continuous) case.

Bounded functions in $\mathcal{V}$ can be approximated by bounded and continuous functions.

Lemma 2. If $h \in \mathcal{V}$ is bounded, then $\exists$ bounded and continuous functions $g_n$ such that
$$
\mathbb{E} \left[ \int_{S}^{T} (h - g_n)^2 \mathrm{d}t \right] \rightarrow 0, \text{as } n \rightarrow \infty
$$

Proof of Lemma 2.

Suppose $h$ is bounded by $M$, first $\phi_n : \mathbb{R} \rightarrow \mathbb{R}$ is constructed as follows:

  1. $\phi_n(x) =0 $ for $x \le -\cfrac{1}{n}$ and $x \ge 0$.
  2. $\int_{-\infty}^{\infty} \phi_n(x) \mathrm{d}x = 1$.

Then define $g_n$ as

$$
g_n(t, \omega) = \int_{-\infty}^{\infty} \phi_n(t-s) h(s, \omega) \mathrm{d}s
$$

Then $g_n$ is bounded and continuous for each $\omega$. And $g_n$ is $\mathcal{F}_t$-measurable for each $t$ since $h$ is $\mathcal{F}t$-measurable. Also $\phi_n$ and $g_n$ are seleted for
$$
\int{S}^{T} (h - g_n)^2 \mathrm{d}t \rightarrow 0, \text{as } n \rightarrow \infty
$$

  • $\phi_n$:
  • $h$:
  • $g_n$ ($n=5$):

Step 3

Handle the general case.

Every function in $\mathcal{V}$ can be approximated by bounded functions.

Lemma 3. If $f \in \mathcal{V}$, then there exists a sequence of bounded functions $h_n \in \mathcal{V}$ such that

$$
\mathbb{E} \left[ \int_{S}^{T} (f - h_n)^2 \mathrm{d}t \right] \rightarrow 0, \text{as } n \rightarrow \infty
$$

Proof of Lemma 3.

For each $n$, let $h_n$ satisfy
$$
h_n(t, \omega) = \begin{cases}
f(t, \omega), & |f(t, \omega)| \le n \
n, & f(t, \omega) > n \
-n, & f(t, \omega) < -n
\end{cases}
$$

By Dominated Convergence Theorem, we have the desired result.

Definition of Ito Integral

Definition 1. If $f \in \mathcal{V}$, one can find a sequence of elementary functions $\phi_n \in \mathcal{V}$ such that

$$
\mathbb{E} \left[ \int_{S}^{T} (f - \phi_n)^2 \mathrm{d}t \right] \rightarrow 0, \text{as } n \rightarrow \infty
$$

Then we define the Ito integral of $f$ as

$$
\int_{S}^{T} f(t, \omega) \mathrm{d}B_t = \lim_{n \rightarrow \infty} \int_{S}^{T} \phi_n(t, \omega) \mathrm{d}B_t
$$

The limit exists in $L^2(\Omega)$ since $L^2(\Omega)$ is complete and

Denote $J_n(\omega) = \int_{S}^{T} \phi_n(t, \omega) \mathrm{d}B_t$, then

$$
J_{n+k}(\omega) - J_n(\omega) = \int_{S}^{T} (\phi_{n+k} - \phi_n) \mathrm{d}B_t
$$

DeltaGrad - Rapid Re-Training of Machine Learning Models

DeltaGrad: Rapid Re-Training of Machine Learning Models

有很多关于模型重新训练和更新的工作。最近，由于人本主义AI、数据机密性和隐私的全球努力（例如欧洲联盟的《通用数据保护条例》），这方面引起了关注（European Union, 2016）。该条例规定，用户可以要求从当前AI系统的分析中删除其数据。所需的保证要求比差分隐私提供的要强（差分隐私可能会在模型中保留数据点的一定贡献，Dwork等人，2014），或者针对数据中毒攻击的防御（仅要求在攻击之后模型的性能不降低，Steinhardt等人，2017）。对于许多其他应用，例如模型解释性和模型调试，高效的数据删除也至关重要。例如，许多现有数据系统（Doshi-Velez和Kim，2017；Krishnan和Wu，2017）必须通过每次删除不同的训练数据子集进行重复训练，以了解这些删除的数据对模型行为的影响。这也接近于删除诊断，通过删除训练集中的数据点，针对ML模型确定最有影响力的数据点，可以追溯到（Cook, 1977）。一些最近的工作（Koh和Liang, 2017）针对通用的机器学习模型，但需要显式维护Hessian矩阵，只能处理一个样本的删除，因此对于许多大规模应用不适用。对于线性模型，基于矩阵逆的有效的rank one更新方法是可行的（例如，Birattari等人，1999；Horn和Johnson，2012；Cao和Yang，2015等）。如果使用线性特征嵌入，无论是随机的还是通过预训练学习的线性特征嵌入，都可以扩展线性方法的范围。已经提出了支持向量机（Syed等人，1999；Cauwenberghs和Poggio，2001）和最近邻（Schelter, 2019）的更新方法。Ginart等人（2019）提出了数据擦除完整性的定义，并提出了一种基于量化的k-means聚类算法来实现。他们还提出了几个能够实现高效模型更新的原则。Guo等人（2019）提出了一种保证随机化算法可以从机器学习模型中删除数据的一般性理论条件。他们的随机化方法需要对标准算法（例如逻辑回归）进行修改才能应用。（Bourtoule等人，2019）提出了用于“取消学习”的SISA（或分片、隔离、切片、汇总）训练框架，其依赖于类似分布式训练的思想。该方法要求将训练数据分成多个分片，以使训练点仅包含在少量分片中。我们的方法依赖于大规模优化，这有着庞大的文献基础。随机梯度方法可以追溯到Robbins和Monro（1951）。最近，许多工作（例如Bottou, 1998；2003；Zhang, 2004；Bousquet和Bottou, 2008；Bottou, 2010；Bottou等人, 2018）专注于经验风险最小化。SGD的收敛证明是基于期望残差的收缩。它们基于一些假设，如方差有界、强或弱增长、平滑性、凸性（或Polyak-Lojasiewicz）、单个和整体损失函数的等等。例如，参见（Gladyshev, 1965；Amari, 1967；Kul’chitskiy和Mozgovoy, 1992；Bertsekas和Tsitsiklis, 1996；Moulines和Bach, 2011；Karimi等人, 2016；Bottou等人, 2018；Gorbunov等人, 2019；Gower等人, 2019）等及其引用。我们的方法类似，但技术细节非常不同，并与拟牛顿方法（如L-BFGS，Zhu等人，1997）更为相关。 🔤1.1.相关工作🔤

“1.1. Related work” (Wu et al., 2020, p. 2) (pdf)

机器学习模型并非静态的，可能需要在稍微改变的数据集上进行重新训练，例如添加或删除一组数据点。这有许多应用，包括隐私保护、鲁棒性、偏差降低和不确定性量化。然而，从头开始重新训练模型是昂贵的。为了解决这个问题，我们提出了一种名为DeltaGrad的算法，通过在训练阶段缓存的信息来快速重新训练机器学习模型。我们提供了理论和实证支持，表明DeltaGrad的有效性，并且与现有技术相比具有优势。

“Machine learning models are not static and may need to be retrained on slightly changed datasets, for instance, with the addition or deletion of a set of datapoints. This has many applications, including privacy, robustness, bias reduction, and uncertainty quantification. However, it is expensive to retrain models from scratch. To address this problem, we propose the DeltaGrad algorithm for rapid retraining machine learning models based on information cached during the training phase. We provide both theoretical and empirical support for the effectiveness of DeltaGrad, and show that it compares favorably to the state of the art.” (Wu et al., 2020, p. 1) (pdf)

机器学习模型的使用越来越普遍，而且很少是静态的。当数据集发生轻微变化时，可能需要在稍微改变的数据集上重新训练模型，例如添加或删除一些数据点。这在许多应用中都有很多用途，包括隐私保护、鲁棒性、偏差降低和不确定性量化。例如，出于隐私和鲁棒性的原因，可能需要从训练数据中删除某些数据点。构建一些删除了某些数据点的模型也可用于构建校正偏差的模型，例如使用jackknife重采样（Quenouille, 1956），需要在所有的留一法数据集上重新训练模型。此外，通过在数据子集上重新训练模型可以用于不确定性量化，例如通过符合预测（conformal prediction）构建统计上有效的预测区间，例如Shafer和Vovk（2008）。然而，从头开始重新训练模型是昂贵的。大规模模型最常用的训练机制是基于（随机）梯度下降（SGD）及其变体。在稍微不同的数据集上重新训练模型将涉及重新计算整个优化路径。当添加或删除少量数据点时，这可能与原始训练过程的复杂性相同。然而，我们期望两个相似的数据集上的模型是相似的。如果我们在许多不同的新数据集上重新训练模型，通过缓存有关原始数据的训练过程的一些信息并计算“更新”可能更有效。最近已经有一些相关的工作，例如Ginart等人（2019）、Guo等人（2019）和Wu等人（2020）。然而，现有方法存在各种限制：它们只适用于特定的问题，如k-means（Ginart等人，2019）或逻辑回归（Wu等人，2020），或者需要额外的随机化导致非标准的训练算法（Guo等人，2019）。为了解决这个问题，我们提出了DeltaGrad算法，用于在训练数据集发生轻微变化时（例如删除或添加样本）快速重新训练机器学习模型，该算法基于训练期间缓存的信息。DeltaGrad解决了先前工作的几个限制：它适用于使用SGD进行经验风险最小化定义的通用机器学习模型，并且不需要额外的随机化。它基于“通过数据微分优化路径”的思想，受到拟牛顿方法的启发。我们在理论和实证上都对DeltaGrad的有效性提供了支持。我们证明它在强凸目标上以快速速度逼近真实的优化路径。我们通过实验证明它在一些中等规模的标准数据集上的准确性和速度，包括两层神经网络。加速比可以高达6.5倍，准确性损失可以忽略不计（见图1）。这为大规模、高效、通用的数据删除/添加机器学习系统铺平了道路。我们还说明了它在上述几个应用中的用途。

“1. Introduction” (Wu et al., 2020, p. 1) (pdf)

贡献我们的贡献包括：DeltaGrad：我们提出了DeltaGrad算法，用于在数据发生轻微变化（添加或删除少量点）时快速重新训练（随机）梯度下降方法的机器学习模型。理论支持：我们提供了理论结果，展示了DeltaGrad的准确性。无论是对于GD还是SGD，我们都证明了误差比删除的点的分数的次序小。实证结果：我们提供了对DeltaGrad的速度和准确性的实证结果，包括添加、删除和连续更新的几个标准数据集。应用：我们描述了DeltaGrad在机器学习中的几个问题中的应用，包括隐私、鲁棒性、去偏和统计推断。

“Contributions” (Wu et al., 2020, p. 2) (pdf)