Time Series代写 machine learning代写 Logistic Regression代写 task代写

Homework 3 INF 552, Instructor: Mohammad Reza Rajati

Time Series代写 An interesting task in machine learning is classification of time series. In this problem, we will classify the activities

1.Time SeriesClassification Time Series代写

An interesting task in machine learning is classification of time series. In this problem, we will classify the activities of humans based on time series obtained by a Wireless Sensor Network.

(a)Download the AReM data from: https://archive.ics.uci.edu/ml/datasets/ Activity+Recognition+system+based+on+Multisensor+data+fusion+\ 28AReM\ 29 . The dataset contains 7 folders that represent seven types of activities. In each folder, there are multiple files each of which represents an instant of a human performing an Each file containis 6 time series collected from activities of the same person, which are called avg rss12, var rss12, avg rss13, var rss13, vg rss23, and ar rss23. There are 88 instances in the dataset, each of which con- tains 6 time series and each time series has 480 consecutive values.Time Series代写

(b)Keep datasets 1 and 2 in folders bending1 and bending 2, as well as datasets 1, 2,and 3 in other folders as test data and other datasets as train data.

(c)FeatureExtraction Time Series代写

Classification of time series usually needs extracting features from them. In this problem, we focus on time-domain features.

i.Research what types of time-domain features are usually used in time series classificationand list them (examples are minimum, maximum, mean, etc).

ii.Extract the time-domain features minimum, maximum, mean, median, stan- dard deviation, first quartile, and third quartile for all of the 6 time series in each instance. You are free to normalize/standardize features or use them ¹

Your new dataset will look like this:

Instance	min₁	max₁	mean₁	median₁ · · · 1st quart₆	3rd quart₆
1
2				Time Series代写
3
.	.	.	.	. . . . .	.
88

where, for example, 1st quart₆, means the first quartile of the sixth time series in each of the 88 instances.Time Series代写

iii.Estimate the standard deviation of each of the time-domain features you extracted from the data. Then, use Python’s bootstrapped or any other method to build a 90% bootsrap confidence interval for the standarddeviation of each

iv.Use your judgement to select the three most important time-domain features (one option may be min, mean, andmax).

(d)Binary Classification Using LogisticRegression^{2 Time Series代写}

1You are welcome to experiment to see if they make a difference.

2Some logistic regression packages have a built-in L₂ regularization. To remove the effect of L₂ regular- ization, set λ = 0 or set the budget C → ∞ (i.e. a very large value).

i.Assume that you want to use the training set to classify bending from other activities, i.e. you have a binary classification problem. Depict scatter plots of the features you specified in 1(c)iv extracted from time series 1, 2, and 6 of eachinstance, and use color to distinguish bending other activities. (See 129 of thetextbook).^{3Time Series代写}

ii.Break each time series in your training set into two (approximately) equal length time series.

Now instead of 6 time series for each of the training instances, you have 12 time series for each training instance. Repeat the experiment in 1(d)i, i.e depict scatter plots of the features extracted fromboth parts of the time series 1,2, and 12. Do you see any considerable difference in the results with those of 1(d)i?

iii.Break each time series in your training set into l 1, 2, . . . , 20time series of approximately equal length and use logistic regression⁴to solve the binary classification problem, using time-domain features. Remember that breaking each of the time series does not change the number of instances. It only changes the number of features for each instance. Calculate the p-values for your logistic regression parameters in each model corresponding to each value of l and refit a logistic regression model using your pruned set of features.Time Series代写

⁵ Alternatively,

you can use backward selection using sklearn.feature selection or glm in Use 5-fold cross-validation to determine the best value of the pair (l, p), where p is the number of features used in recursive feature elimination. Explain what the right way and the wrong way are to perform cross-validation in this problem.⁶ Obviously, use the right way! Also, you may encounter the problem of class imbalance, which may make some of your folds not having any instances of the rare class. In such a case, you can use stratified cross validation. Research what it means and use it if needed.In the following, you can see an example of applying Python’s Recursive Feature Elimination, which is a backward selection algorithm, to logistic re- gression.Time Series代写

# R e c u r s i v e Fe a tu r e E l i m i n a t i o n from s k l e a r n i mpo rt d a t a s e t s

from s k l e a r n . f e a t u r e s e l e c t i o n i mpo rt RFE

from s k l e a r n . l i n e a r m o d e l i mpo rt L o g i s t i c R e g r e s s i o n # l o a d th e i r i s d a t a s e t s

d a t a s e t = d a t a s e t s . l o a d i r i s ( )

3You are welcome to repeat this experiment with other features as well as with time series 3, 4, and 5 in each instance.

4If you encountered instability of the logistic regression problem because of linearly separable classes, modify the Max-Iter parameter in logistic regression to stop the algorithm immaturely and prevent from its instability.

5R calculates the p-values for logistic regression automatically.

One way of calculating them in Python is to call R within Python. There are other ways to obtain the p-values as well.Time Series代写

6This is an interesting problem in which the number of features changes depending on the value of the parameter l that is selected via cross validation. Another example of such a problem is Principal Component Regression, where the number of principal components is selected via cross validation.

# c r e a t e a b a s e c l a s s i f i e r used to e v a l u a t e a s u b s e t o f a t t r i b u t e s model = L o g i s t i c R e g r e s s i o n ( )

# c r e a t e th e RFE model and s e l e c t 3 a t t r i b u t e s r f e = RFE( model , 3 )

r f e = r f e . f i t ( d a t a s e t . data , d a t a s e t . t a r g e t ) # summarize th e s e l e c t i o n o f th e a t t r i b u t e s p r i n t ( r f e . s u p p o r t )

p r i n t ( r f e . r a n k i n g )

iv.Report the confusion matrix and show the ROC and AUC for your classifier on train data. Report the parameters of your logistic regression β_i’s as well as the p-values associated with

v.Test the classifier on the test set. Remember to break the time series in your test set into the same number of time series into which you broke your training set. Remember that the classifier has to be tested using the features extracted from the test set. Compare the accuracy on the test set with the cross-validation accuracy you obtained Time Series代写

vi.Do your classes seem to be well-separated to cause instability in calculating logistic regressionparameters?

vii.From the confusion matrices you obtained, do you see imbalanced classes? If yes, build a logistic regression model based on case-control sampling and adjust its parameters. Report the confusion matrix, ROC, and AUC of the model.

(e)Binary Classification Using L₁-penalized logisticregression

i.Repeat 1(d)iii using L₁-penalized logistic regression,⁷e. instead of using p- values for variable selection, use L₁ regularization. Note that in this problem, you have to cross-validate for both l, the number of time series into which you break each of your instances, and λ, the weight of L₁ penalty in your logistic regression objective function (or C, the budget). Packages usually perform cross-validation for λ automatically.^{8Time Series代写}

ii.Compare the L₁-penalized with variable selection using p-values. Which one performs better? Which one is easier toimplement?

(f)Multi-class Classification (The RealisticCase)Time Series代写

i.Find the best l in the same way as you found it in 1(e)i to build an L₁– penalized multinomial regression model to classify all activities in yourtrain- ing set.⁹ Report your test error. Research how confusion matrices and ROC curves are defined for multiclass classification and show them for this problem if ¹⁰

ii.Repeat 1(f)i using a Na¨ıve Bayes’ Use both Gaussian and Multi- nomial priors and compare theresults.

7For L₁-penalized logistic regression, you may want to use normalized/standardized features Time Series代写

8Using the package Liblinear is strongly recommended.

9New versions of scikit learn allow using L₁-penalty for multinomial regression.

10For example, the pROC package in R does the job.

iii.Which method is better for multi-class classification in this problem?

2.ISLR7.4

3.ISLR, 4.7.3

4.ISLR 4.7.7

5.Extra Practice (you do not need to submit the answers): ISLR 3.7.3, 3.7.5, 4.7.4, 4.7.9

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