Jun's Blog
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Recent content on Jun's BlogHugo -- gohugo.ioen-usFri, 19 Jul 2019 00:00:00 +0000Bookdown Epub rendering
/2019/07/19/bookdown-epub-rendering/
Fri, 19 Jul 2019 00:00:00 +0000/2019/07/19/bookdown-epub-rendering/ Epub rendering Install dependency packages go to directory that contains index.Rmd
devtools::install_deps() Render book at console bookdown::render_book("", "bookdown::epub_book") look at yml files _bookdown.yml rmd.files You can use Build not knit Refer to this https://github.com/christophM/interpretable-ml-book
Linear representation of integral
/2019/07/09/linear-representation-of-integral/
Tue, 09 Jul 2019 00:00:00 +0000/2019/07/09/linear-representation-of-integral/ Linear representaion of integral Riesz Representation Theorem one of measure property
\(\Lambda f = \int f\) \(du\) \(for\) \(every\) \(f \in C_c (X)\)
\(f = \Sigma_1^nC_i1_{E_i}(x)\)
\(\Lambda f = \Sigma_1^nC_i1_{E_i}(x) \mu(E_i) = \int f du\)
\(\Lambda = vector(\mu(E_i))\)
Outer measure, Caratheodory extension theorem
/2019/07/06/outer-measure-caratheodory-extension-theorem/
Sat, 06 Jul 2019 00:00:00 +0000/2019/07/06/outer-measure-caratheodory-extension-theorem/ Measure \(\mu\) Anyhow measure, nice property is liberty.
Elementary measure, nice property are monotonicyty and finite subadditivity.
Outer measure \(\mu^*\) \(\mu^* : 2^X \rightarrow [0, +\infty]\)
\(\mu^* = inf\{ \mu_0 (\cup^\infty_{k=1} A_k): E \subset \cup^\infty_{k=1} A_j \}\)
Collection of measurable sets Anyhow \(2^X\)
Algebra
Caratheodory
Urysohn's lemma
/2019/06/18/urysohns-lemma/
Tue, 18 Jun 2019 00:00:00 +0000/2019/06/18/urysohns-lemma/Support The support of complex function \(f\) on a topological space \(X\) is a closer of the set \({x: f(x) \neq 0}\)
\(C_c(X)\) denotes the collection of all continuous complex function whose support is compact.
\(C_c(X)\) is vector space because \(C_c(X)\) is closed under addition and multiplication.
\(K\prec f\) denotes the \(K\) is compact subset of X, that \(f \in C_c(X)\) that \(0 \leq f(X) \leq 1\) for all \(x \in X\) and that \(f(X) = 1\) for all \(x \in K\)Local basis
/2019/06/17/local-basis/
Mon, 17 Jun 2019 00:00:00 +0000/2019/06/17/local-basis/ Local basis Local basis used for limit like this (((((((((()))))))))). A topological space can define limit if the space has countable local basis.
Definition of local basis A collection \(\mathfrak{B}\) of Neiborhood of \(x\) such that every neiborhood of \(x\) which contains at least one element of \(\mathfrak{B}\)
Neiborhood system, Neiborhood filter (view of local basis) Open set with neiborhood filter
connected space compact space
/2019/06/09/connected-space-compact-space/
Sun, 09 Jun 2019 00:00:00 +0000/2019/06/09/connected-space-compact-space/Conneted space If there are disjoint open subsets \(U \cup V = X\). The space X is disconnected. Otherwise connected.
Path connected space Every elements \(x,y \in X\) have image of \(f:[a,b] \rightarrow X\) that \(f(a) = x, f(b)=y\) is in \(X\).
Component Relation class \([x]\) is a subset of of \(X\) those elements is also elements of connected subspaces of containing \(x\). Connected space has only one component.Position of fig and table in RMarkdown pdf
/2019/05/31/position-of-fig-and-table-in-rmarkdown-pdf/
Fri, 31 May 2019 00:00:00 +0000/2019/05/31/position-of-fig-and-table-in-rmarkdown-pdf/Rmarkdown pdf rendering defalt setting of figure and table is top of the page. This location is not where I intend.
knitr::chunk_option fig.pos = “H” makes that the figure puts at current location.
For table, latex_options = “hold_position” in kabel_styling argument puts at current locationInsert Image in Windows
/2019/05/30/insert-image-in-windows/
Thu, 30 May 2019 00:00:00 +0000/2019/05/30/insert-image-in-windows/In windows, insert image addin does not work.
Trobule shooting
1) make directory manually (/static/post/insert-image-in-windows_files).
2) do addin.
3) no image error message will apprear.
4) save Rmd and serve site. This will save you.Beamer works best on Linux
/2019/05/29/beamer-works-best-on-linux/
Wed, 29 May 2019 00:00:00 +0000/2019/05/29/beamer-works-best-on-linux/ Beamer does not render well on Windows platform Insertion image Image size conrol Make slide on Linux platform !! Limit
/2019/05/29/limit/
Wed, 29 May 2019 00:00:00 +0000/2019/05/29/limit/Limits \(\epsilon\) method sequence \(S_n\) goes to infinite \(L\) is limit of \(S_n\), iif there is \(N\) satisfing \(S_n\) \(-\) \(L < \epsilon\) in every \(n>N\). Upper limit \(\lim_{n\to\infty}\) \(sup(a_n)\) Lower limit \(-\lim_{n\to\infty}\) \(inf(a_n)\) Limit of function \(f_n\) \((x)\) \(=x^n\) (\(n \in N\))
\(f_n\) \(:(0,1) \rightarrow (0,1)\)
Pointwise limit \(\lim_{n\to\infty}\) \(f_n\) \((x)\) \(=f(x) = 0\) for every \(x\)Lebesgue measure
/2019/05/27/lebesgue-measure/
Mon, 27 May 2019 00:00:00 +0000/2019/05/27/lebesgue-measure/Lebesgue measure Jordan measure: finite union of element sets (boxes)
Lebesgue measure: conutable union of element sets (boxes)
Properties of Lebesgue measure Monotonicity
Subadditivity Simple function Finite linear combination of measurable set
\(C_1\)\(1_{E_1}\) \(+\) \(C_2\)\(1_{E_2}\) \(...\) \(+\) \(C_k\)\(1_{E_k}\) where \(1_{E_k}\) is identity function
Uniform convergence Sequence of function \(f_n\)\((x)\) is uniform convergence, if \(lim_{n\rightarrow \inf}\) \(Sup\)
\(Sup\) is the point in uniform convergencePredictive modeling
/2019/05/27/predictive-modeling/
Mon, 27 May 2019 00:00:00 +0000/2019/05/27/predictive-modeling/Predictive modeling Lesson from radioimmunology prediction modeling.
First look at the data. The predictive variable names must be identical in both train and test sets.
Output variable should be well defined. Unvalenced?
Look at the missing values. Consider imputation Preprocessing Resolving skewness Box-Cox transformation should be done in non-negative varialbes.
Use Yeo-Johnson transformation for variables including negative value. Errors when prediction of test set “pred method can not take rf object” like error means random forest (rf) modeling fails.Topology subject
/2019/05/26/topology-subject/
Sun, 26 May 2019 00:00:00 +0000/2019/05/26/topology-subject/Topology subjects Topology \(\tau\) has many concepts. In this post, I’ll summarize the concepts in topology.
Topology \(\tau\) defines subsets that contains close elements. The closeness makes other properties related with subsets.
Topological space is a set defined with topology \(\tau\).
-Matric topological space
-Cofinite topological space
-Subspace topology
Basis for a topology Basis \(B\) is a family set of subsets that construct topology \(\tau\).
Closed set and limit points Closed set is complement of open set.Addins
/2019/05/25/addins/
Sat, 25 May 2019 00:00:00 +0000/2019/05/25/addins/ Writing a contents by addins Problum: plain RMarkdown file display was not good. Date and author were not valid.
This is exercise write a contents by addins.
It makes valid YAML and automatically saved in contents post directory.
Measure and Topology
/2019/05/25/measure/
Sat, 25 May 2019 00:00:00 +0000/2019/05/25/measure/Measure and Topology Both are family of subset with properties measurable set is called \(\sigma\) algebra Algebra Algebra usually means system of operations like \(+\), \(\times\).
Measure problem Which set can be measure? What makes measurable?
How to measure? Topology Something like catergory
countable intersections and albitary unions
What purpose of the topology?
Analysis, continuous function. limits of sequences.About
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Thu, 05 May 2016 21:48:51 -0700/about/This is a Jun’s website