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原创 Yang不等式，Hölder不等式与闵可夫斯基(Minkowski)不等式
Yang不等式∀a,b≥0,p,q>0,∀a,b≥0,p,q>0,\forall a, b \ge 0, p, q\gt 0, 若 1p+1q=1,1p+1q=1,\dfrac{1}{p} + \dfrac{1}{q} = 1, 则： ab≤app+bqq,ab≤app+bqq,ab \le \dfrac{a^p}{p} + \dfrac{b^q}{q}, 且当且仅当 ap=...
2017-10-29 22:22:33
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原创 gRPC
Protocol buffer data is structured as messages, where each message is a small logical record of information containing a series of name-value pairs called fields.Service method: Unary RPC Server s...
2018-08-21 17:13:03
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原创 Deep Learning Notes: Chapter 1 Introduction
前言最近开始读《Deep Learning》一书。这让我有了一个边读书边写笔记的动机：很有必要有一个笔记，能够让人很轻松流畅的读懂这本书的核心内容，至少可以把握住这本书的脉络。 由于终究是英文表达更地道，因此该笔记都是节选自书中的原文。各位读者如果有建议或意见，欢迎留言。谢谢！Deep Learning Chapter 1 Introduction Concept Des...
2018-08-18 20:16:48
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原创 Pro Git Notes
Git is a Distributed Version Control Systems (DVCSs). Clients fully mirror of the repository, including its full history.
2018-08-12 01:38:23
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原创 多元函数的牛顿迭代法
f(X)=f(X0)+f′(X0)ΔX+12(ΔX)Tf″(X0)ΔXf(X)=f(X0)+f′(X0)ΔX+12(ΔX)Tf″(X0)ΔXf(X) = f(X_0) + f'(X_0) \Delta X + \dfrac {1} {2} \left ( \Delta X \right ) ^T f''(X_0) \Delta X 于是 f′(X)=f′(X0)+f″(X0)ΔXf′(X)=f′...
2018-08-09 17:55:05
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原创 牛顿迭代法
若 x=F(x)x=F(x)x = F(x) 等价于 f(x)=0f(x)=0f(x) = 0 则F(x)F(x)F(x) 称为迭代函数。f(x)f(x)f(x) 有二阶连续导数，且 f′(x)≠0f′(x)≠0f'(x) \neq 0 则 ∀x0,x∈R,∀x0,x∈R,\forall x_0, x \in \mathbb R, 若 f(x0)=0f(x0)=0f(x_0) = 0 则 ...
2018-08-09 09:02:05
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原创 Nesterov Momentum
x_ahead = x + mu * v# evaluate dx_ahead (the gradient at x_ahead instead of at x)v = mu * v - learning_rate * dx_aheadx += v=>x_prev = xv_prev = vx_ahead = x_prev+ mu * v_prev v = mu * v_...
2018-08-09 08:19:11
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原创 CS231n Note
CS231n NoteConcepts Concept Description Image Classification Object Detection Action Classification Image Captioning Semantic Segmentation Perceptual ...
2018-08-04 20:56:43
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原创 Clockwise/Spiral Rule to parse C declaration
http://c-faq.com/decl/spiral.anderson.html
2018-05-01 18:32:17
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原创 推荐系统
推荐方式社会化推荐（social recommendation） 基于内容的推荐（content-based filtering） 协同过滤（collaborative filtering）推荐系统评测推荐系统试验方法离线试验 用户调查 在线试验（AB测试）评测指标用户满意度预测准确度覆盖率多样性新颖性惊喜度（serendipity）信任度实时性...
2018-04-25 21:52:44
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原创 机器学习的求导公式
机器学习的求导公式损失函数的求导公式设 loss(X)loss(X)\operatorname {loss} \left (X\right ) 为单个样本 XXX 的损失函数， A=g(Z)=⎛⎝⎜⎜g(z1)⋮g(zn)⎞⎠⎟⎟A=g(Z)=(g(z1)⋮g(zn))A = g\left (Z\right ) = \begin{pmatrix} \operatorname {g...
2018-04-18 12:30:10
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原创 Recurrent Neural Networks
Examples of Sequence DataSpeech RecognitionMusic GenerationSentiment ClassificationDNA Sequence AnalysisMachine TranslationVideo Activity RecognitionName Entity RecognitionNotation ...
2018-04-16 06:28:37
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原创 Neural Style Transfer
ConceptContent C + Style S = Generated image GWhat are Deep ConvNet Learning?More abstract features in deeper layer.Cost Functionloss(G;C,S)=αlosscontent(S,G)+βlossstyle(C,G)loss(G;C,...
2018-04-16 00:04:20
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原创 Face Recognition
Face Verification vs Face Recognition Name Input Output Description Face Verification Image and Name / ID Is the image the person with this given ID? Face Recognition Ima...
2018-04-15 19:39:30
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原创 Object Detection
Concepts Name Description yyy Object Classification At most one object y=⎛⎝⎜c1c2c3⎞⎠⎟y=(c1c2c3)y = \begin{pmatrix} c_1 \\ c_2 \\ c_3 \end{pmatrix} Object Localization At most ...
2018-04-15 19:17:33
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原创 Convolutional Neural Networks
PaddingOutput Dimensionn+2p−f+1n+2p−f+1n + 2 p - f + 1Padding TypesValid: p=0p=0p = 0 Same: n+2p−f+1=n⇒p=f−12n+2p−f+1=n⇒p=f−12n + 2 p - f + 1 = n \Rightarrow p = \dfrac {f - 1} {2}Str...
2018-04-13 01:34:11
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原创 Learning from Multiple tasks
Where Transfer Learning from A to B Makes SenseTask A and B have the same input X.You have a lot more data for A than B.Low level features in A could be helpful for learning B.Where Multi-task...
2018-04-12 23:37:42
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原创 Bias and Variance with Mismatched Distributions
Bias and Variance with Mismatched Distributions
2018-04-12 22:08:00
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原创 Softmax Function
Sigmoid Functionsigmoid(z)=11−e−zsigmoid(z)=11−e−z\operatorname {sigmoid} (z) = \dfrac {1} {1 - e ^{-z}}Softmax Functionsoftmax(zi;Z)=ezi∑i=1nezi,1≤i≤nsoftmax(zi;Z)=ezi∑i=1nezi,1≤i≤n\operato...
2018-04-11 22:13:26
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原创 Momentum, RMSprob and Adam
Gradient Descent with MomentumCompute exponentially weighed average of gradient, and use the gradient to update weights.AlgorithmOn iteration t:Compute dWdW\operatorname {d} W and dbdb\op...
2018-04-11 02:03:54
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原创 Exponentially Weighted Averages
Exponentially Weighted Averagesvt=βvt−1+(1−β)θtvt=βvt−1+(1−β)θtv _{t} = \beta v _{t - 1} + \left (1 - \beta \right ) \theta _{t} =β[βvt−2+(1−β)θt−1]+(1−β)θt=β[βvt−2+(1−β)θt−1]+(1−β)θt= \beta \lef...
2018-04-11 00:09:48
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原创 Shallow Neural Network Week 3
Single SampleSymbolsX=⎛⎝⎜⎜x1⋮xnx⎞⎠⎟⎟,Y=⎛⎝⎜⎜y1⋮yny⎞⎠⎟⎟,X=(x1⋮xnx),Y=(y1⋮yny),X = \begin{pmatrix} x_1 \\ \vdots \\ x_{n _{x}} \end{pmatrix}, Y = \begin{pmatrix} y_1 \\ \vdots \\ y_{n _{y}} \end{pm...
2018-04-04 05:30:25
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原创 Activation function in Neural Network
Logistic / Sigmoid functiong(x)=11+e−x=ex1+exg(x)=11+e−x=ex1+exg(x) = \dfrac {1} {1 + e ^{-x}} = \dfrac {e ^{x}} {1 + e ^{x}} g(−x)=11+ex=e−x1+e−xg(−x)=11+ex=e−x1+e−xg(-x) = \dfrac {1} {1 + e ^{x}}...
2018-03-30 19:47:41
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原创 Code to download files from google drive to colab
Code:def download_from_google_drive(file_name_prefix): # 1. Authenticate and create the PyDrive client. auth.authenticate_user() gauth = GoogleAuth() gauth.credentials = GoogleCredentials....
2018-03-26 15:06:02
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原创 多元高斯分布
f(X;μ,Σ)=1(2π)n/2|Σ|1/2exp(−12(X−μ)⊺Σ−1(X−μ))f(X;μ,Σ)=1(2π)n/2|Σ|1/2exp(−12(X−μ)⊺Σ−1(X−μ))f\left (X ; \mu , \Sigma\right ) = \dfrac {1} {{\left (2 \pi\right )} ^ {n / 2} {\vert \Sigma \vert } ^ {1 / ...
2018-03-24 01:08:19
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原创 一元高斯分布
f(x;μ,σ)=12π−−√σe−(x−μ)22σ2f(x;μ,σ)=12πσe−(x−μ)22σ2f\left (x; \mu, \sigma \right ) = \dfrac {1} {\sqrt {2 \pi} \sigma} e ^ { - \dfrac {\left (x - \mu\right ) ^2} {2 \sigma ^2} } f(μ;μ,σ)=12π−−√σ,f(μ±...
2018-03-23 00:16:02
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原创 Support Vector Machine's Large Margin
SVM Cost FunctionJ(θ)=C∑i=1m[yicost1(W⊺Xi+θ0)+(1−yi)cost0(W⊺Xi+θ0)]+∑j=1nλ2θ2jJ(θ)=C∑i=1m[yicost1(W⊺Xi+θ0)+(1−yi)cost0(W⊺Xi+θ0)]+∑j=1nλ2θj2J\left (\theta \right ) = C \sum \limits_{i = 1} ^{m} \le...
2018-03-19 12:20:55
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原创 Cost Function of Support Vector Machine
Logistic Regression 中的函数 f,gf,gf, gf(x)=ln(1+ex),x∈R,g(x)=f(−x)f(x)=ln(1+ex),x∈R,g(x)=f(−x)f(x) = \ln (1 + e ^{x}), x \in \mathbb R, g(x) = f(-x)f,gf,gf, g 的性质f′(x)=ex1+ex>0,x∈Rf′(x)=ex1+e...
2018-03-18 19:05:27
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原创 Reason of Random Initialization - Neural Networks
Symmetry Problem若对于神经网络任意一层 l,l,l, 该层所有参数 ωli,jωi,jl\omega ^{l} _{i,j} 的初始值都一样，则在梯度下降每次迭代中： {ωl−11,j=ωl−12,j,0≤j≤sl−1,ωli,1=ωli,2,1≤i≤sl+1,,2≤l≤L−1{ω1,jl−1=ω2,jl−1,0≤j≤sl−1,ωi,1l=ωi,2l,1≤i≤sl+1,,2...
2018-03-18 14:04:45
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原创 Backpropagation Algorithm 的梯度
损失函数 J(θ)J(θ)\operatorname {J} \left (\mathbf {\theta}\right )J(θ)=−1m∑i=1m∑k=1K[y(i)kln(hθ(X(i))k)+(1−y(i)k)ln(1−hθ(X(i))k)]J(θ)=−1m∑i=1m∑k=1K[yk(i)ln(hθ(X(i))k)+(1−yk(i))ln(1−hθ(X(i))k)]\opera...
2018-03-15 23:49:12
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原创 Cost function of Logistic Regression and Neural Network
Logistic / Sigmoid functiong(x)=11+e−x=ex1+exg(x)=11+e−x=ex1+exg(x) = \dfrac {1} {1 + e ^{-x}} = \dfrac {e ^{x}} {1 + e ^{x}}Cost functionLogistic Regressionhθ(X)=f(X⊺θ)=P(y=1|X;θ)hθ(X)=f(X⊺...
2018-03-12 22:25:59
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原创 Pronunciation Difference between /ʌ/ and /ɑ/
Pronunciation Difference between /ʌ/ and /ɑ/The sound /ʌ/ is pronounced in the following cases:When a word is spelled with the letter “u” in a closed stressed syllable, for example, “luck,” “cup...
2018-03-09 00:39:57
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原创 机器学习的偏差-方差分解
假设样本变量为 XXX ，它的标签 YYY 为 XXX 的函数 Y=f(X)+ϵY=f(X)+ϵY = f\left (X\right ) + \epsilon 。其中为 ϵϵ\epsilon 机器学习模型学习不到的噪音。 对于机器学习模型 M,M,M, 假设训练后，对 XXX 的预测值为 XXX 的函数 f^(X)f^(X)\hat f \left (X \right ) 。 对于一个测试...
2018-02-26 12:08:00
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原创 使用梯度下降与牛顿法求解最小平方和问题
问题已知： hW(X)=∑nj=1wjxj+wn+1=∑n+1j=1wjxj=X⊺W,hW(X)=∑j=1nwjxj+wn+1=∑j=1n+1wjxj=X⊺W,h_{W}(X) = \sum _{j = 1} ^{n} w_j x_j + w_{n + 1} = \sum _{j = 1} ^{n + 1} w_j x_j = X ^{\intercal} W, 其中 W=⎛⎝⎜⎜⎜⎜w...
2018-02-25 21:00:06
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原创 多面集的点的性质
定义设多面集 S={X∈Rn:AX≤b},S={X∈Rn:AX≤b},S = \{ X \in \mathbb R ^n: AX \le b \}, 其中 A=⎛⎝⎜⎜a1⋮am⎞⎠⎟⎟∈Rm×n,A=(a1⋮am)∈Rm×n,A = \begin{pmatrix} a_1\\ \vdots \\ a_m\end{pmatrix} \in \mathbb R ^{m \times n}, ...
2018-02-24 04:39:11
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原创 射线包含于凸集的充要条件
定理对于任意一个凸集 SSS ，对于任意一条射线 L={X0+td⃗ :t≥0},L={X0+td→:t≥0},L = \{ X_0 + t \vec d : t \ge 0\}, 则 L⊆SL⊆SL \subseteq S 当且仅当 X0∈SX0∈S X_0 \in S 且 S∩LS∩LS \cap L 无界。证明必要性易得。充分性∀X∈Rn,∀X∈...
2018-02-24 03:58:47
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原创 多面集的表示定理的必要性的证明
多面集的表示定理的必要性的证明前面的内容见 多面集的表示定理4.2 必要性4.2.1 有界情况下若 SSS 有界，由于有界集没有方向，因此只要证明： ∀X∈S,∀X∈S,\forall X \in S, XXX 可以被表示成 X1,⋯,XkX1,⋯,Xk X_1, \cdots, X_k 的凸组合。 即存在集合 {λi∈R:∑i=1kλi=1,λi≥0,i∈N,1≤i...
2018-02-23 21:06:04
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原创 多面集的方向的性质
多面集的方向的性质引理设向量 X,β,d⃗ ∈V,X,β,d→∈V, X, \beta, \vec d \in V, 1. X≥β,X≥β,X \ge \beta, 则 ∀k∈R,k≥0,X+kd⃗ ≥β⇔d⃗ ≥0⃗ ∀k∈R,k≥0,X+kd→≥β⇔d→≥0→ \forall k \in \mathbb R, k \ge 0, X + k \...
2018-02-21 20:09:47
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原创 多面集的极点的性质
多面集的极点的性质设多面集 S={X∈Rn:AX≤b},S={X∈Rn:AX≤b},S = \{ X \in \mathbb R ^n: AX \le b \}, 其中 A=⎛⎝⎜⎜a1⋮am⎞⎠⎟⎟∈Rm×n,A=(a1⋮am)∈Rm×n,A = \begin{pmatrix} a_1\\ \vdots \\ a_m\end{pmatrix} \in \mathbb R ^{m \tim...
2018-02-21 17:35:53
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原创 线性规划的标准型与规范型 (Standard and Canonical Forms)
线性规划的标准型与规范型 (Standard and Canonical Forms) Form Minimization Problem Maximization Problem Standard mins.t.∑j=1ncjxj∑j=1naijxj=bi,i=1,⋯,mxj≥0,j=1,⋯,nmin∑j=1ncjxjs.t.∑j=1naijxj=bi,i=1,...
2018-02-21 15:17:28
8439
Matrix CookBook
2017-11-02
Pattern Recognition and Machine Learning 中英文+答案
2017-11-02
Machine Learning A Probabilistic Perspective
2017-11-02
数据挖掘导论 高清中文完整版 PDF
2014-06-15
计算机体系结构 — 量化研究方法 英文第五版 Computer Architecture A Quantitative Approach
2014-04-18
Architecting Microsoft .NET Solutions for the Enterprise
2013-06-06
Inside Microsoft SQL Server 2008: T-SQL Querying
2013-06-06
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