jun1-cs 님의 블로그

1. Curse of dimensionality: as the dimension of space gets bigger, required size of data (number of distinct features) gets higher -> the model can be overfitted Use dimension reduction methods => select only important orientation, vector that shows high variance of datapoints-> eliminate unimportant features (noise)Ex) PCA, LDA 2. Principal components analysisEx) input data, X [100,4] -> standa..

ensemble learning: compare multiple classifer models and make better decision to reduce the prediction error 1. Independent ensemble learning: ml models operate in parallel -> fast1) voting: train multiple type of models with train data and vote to classify itEx) plurality voting, majority voting- we can also mathematically prove that n classifiers with same error rate e can exhibit lower or sam..

1. Basic concepts1) line and segmenttwo points x1, x2 -> y=wx1 + (1-w)x2for 0for w1: y is line 2) affine set and convex setaffine set: the set C that contains line wx1 + (1-w)x2 or, w1x1 + w2x2 + w3x3 +...+ wnxn (Sigma(wi)=1)-> affine combination: (w1,w2,...,wn) that belong to set C -> meaning: combination of weights that make y lies on x1~xn points convex set: the set C that contains segment wx..

A logic that represents an ambiguous feature more accurately=> Mathematically implement ambiguous representation of human language (Ex: little bit, very, quite, definitely) Ex) representing age as old / young -> classifying with a single age threshold does not correspond with human's cognitive classification standard: if we set age 70 as a threshold, is age 69 young? -> we must set/assume distri..

* terminologychromosome: the answer of question, form of output of modelgene: basic component of chromosomeencoding: form of answer -> chromosomedecoding: chromosome -> form of answer fitness: the score of how much each chromosome is fit to environment at that time point-> fitness function: use to get score of each chromosome Core concept of genetic algorithm - select chromosomes of high fitness..

1. Radiomics1) predicting binomial prognosis of glioblastoma with MRI imageMRI T1, T2 image -> use 1 axial image penetrating the center of tumor in each patient imagedata: 70 patient data consisting of clinical information and DICOM image -> segmentation of tumor using ImageJ-> define and calculate numercial features using radiomics package in R-> train and test ml model (Ex: Random Forest) - 0/..

1. kNN- select variables based on pca results- normalize (max-min / z norm) each variable- scatter datapoints into space- datapoints -> label O, label X group split- apply kNN alg -> classify label X group, using k nearest datapoints(label O group) * k is odd number! -> to escape the situation where k nearest datapoints show 50:50 proportion of two classes* supervised learning: must use labeled ..

input space -> use linear decision boundaries -> labeled regionsEx) 1~K의 클래스가 존재한다.k번째 클래스를 분류하는 변수, 함수가 fk(x) 라면 fk(x)=bk0+bk^Tx이다. k, l번째 클래스 사이에서 분리 -> fk(x)=fl(x), (bk0-bl0) + (bk-bl)^T x=0 의 affine set, hyperplane이 존재해야 한다. => 이를 위해, x를 특정 클래스로 분류하기 위해서 discriminant function, dk(x) 함수를 이용한다. 위의 식은 x 열벡터와 y 열벡터 사이에서 최적의 계수 행렬인 B를 적합하기 위한 식이다. y_true-y_pred의 제곱의 합이 최소가 되게 하는 B를 찾는 것이므로 MSE를 사..

[The Elements of Statistical Learning] 1. Mixture model: describe the data using mix of multiple simple models (ex: gaussian model)Ex) two-component mixture model Y: combination of two gaussian modelsg(y): density of Y-> sum the log g(y) of N data points -> maximize this log-likelihood Parameters of the model: pi, mu1, s1, mu2, s2 => mixture models -> useful for supervised learning, lead to radi..

[The Elements of Statistical Learning] Bootstrap: Computational way to assess uncertainty.Ex) To fit a cubic spline to the data, we represent seven dimensional linear space (7-spline basis functions)N개의 datapoint, 7개의 함수(다변수라고 생각) -> H[N,7] -> b는 7개의 함수를 더할 때 함수별 가중치를 포함한 행렬 -> b=(H^T H)^(-1) H^T y => bootstrap distribution 이용해서 spline smooth 계산 (95% CI) 1)Parametric bootstrap: gaussian noise + ..