Statistical Learning - Science topic

Please write me pro and contra arguments! 

I conducted a study titled 'The Impact of AI Integration in Statistics Learning on Student Motivation and Learning Engagement in the Higher Education Sector.' The results indicate improvements in student motivation and engagement. Could these findings represent an initial step toward enhancing overall academic performance? I would appreciate your insights.

I possess a series of comprehensive course notes dating back to 2018, each spanning approximately 130 pages. These notes delve into the mathematical aspects of understanding statistical learning. The lectures are tailored for Master's degree students and were delivered by S. Mallat at the Collège de France. Despite being the sole author, Professor Mallat has validated these notes. I believe that sharing them on ResearchGate would enhance their visibility. Please advise if this is feasible.

Best regards,

J.E Campagne

Chalmers in his book: What is this thing called Science? mentions that Science is Knowledge obtained from information. The most important endeavors of science are : Prediction and Explanation of Phenomenon. The emergence of Big (massive) Data leads us to the field of Data Science (DS) with the main focus on prediction. Indeed, data belong to a specific field of knowledge or science (physics, economy, ....).

If DS is able to realize prediction for the field of sociology (for example), to whom the merit is given: Data Scientist or Sociologist?

10.1007/s11229-022-03933-2

#DataScience #ArtificialIntelligence #Naturallanguageprocessing #DeepLearning #Machinelearning #Science #Datamining

In search of latest statistical theory which is backing up the machine learning algorithms.

I'm looking for an algorithm that computes the VC dimension of a given hypothesis class H but I'm still unable someone that is "code-ble". The objective is to compute the minimum size of data needed to achieve PAC learning with a supervised learning model and for a given precision ε and a confidence δ.

What are the best methods to handle Imbalance data? and Do these methods make more biasness?

I have a dataset with 19 training points and 6 testing points.

At first I defined the rules for 19 training sets and then tried making predictions for the rest of 6 points. But I got all constant values.

Then when I added 6 more rules, I started getting the values which were very close to the actual values.

My question is do I have to define the rest 6 rules too? Because if I do that then it undermines the intuition of "Testing".

Or do I have to reduce the levels for output Data? Because I have created 5 levels for the output data (Extremely low, Low, Medium, High, Extremely high)

Any help would mean a lot!

In Statistical Learning Theory, Uniform convergence means for a hypothesis class H, given m(\delta, \epsilon), for arbitrary distribution over domain (X, Y), with probability $1- \delta$, the generalization error is within $\epsilon$ range.

Now The no free lunch theorem state that one can construct a distribution over (X,Y) such that an algorithm will fail with large probability while another algorithm will work. The sample size is m smaller than half of cardinality of X.

My question is: are the two statements contradictory? If the uniform convergence hold, algorithm A working on hypothesis class H will always work as long as the sample complexity is reached, so there would not be cases of failure?

I wonder if there is any explanation that which of statistical learning or machine learning may work better and what is reason for that.

Bayesian updating and and Bayesian networks are used in so many machine learning algorithms, but can we consider them as machine learning techniques? and if we can, under what circumstances? and in what kind of applications?

Suppose we deal with a dataset with different kind of attributes (numeric and nominal) and binary class. How can we find a unique number as the shannon entropy of this dataset (as a presentation of kolmogorov complexity of this dataset)?

Is there any literature that focuses on design of the classifier theoretically, without considering metrics.

I need a reference to the integral analogue of Cauchy-Binet identity, but I can not find such a reference. Could you please help me? Thank you in advance.

If the data for the classes is imbalanced what are the best machine learning algorithms and will he choice vary in the case of binary and multi-class classification

Does anyone have a graphical representation/explanation of the difference between ANOVA, ANCOVA, MANOVA and MANCOVA?

is it possible to use statistical learning to get results on thermodynamics, heat transfer, and fluid dynamics,  ... etc,, some phenomenons are still complicated and without experiments, there is no way to get their results.   

Hi researchers!  I am a learner of statistics learing and machine learning. After applying the Convolutional neural networks into image recognition and text mining, I think this method is powerful in classification.  So I want to apply them into statistics field and want to know the advantages and disadvantages of CNNs. Can I view it as a specia kind of "regression", which is blessed with flexible model form and interaction form？ What is the disadvantage of it? Thank you very much!

If any reference material please provide to me

How can machine learning or statistical learning techniques be used in association rule mining?

Regarding the problem of graph coloring, is there any good reference dialing with the VC dimension of the problem ?

More generally: concerning NP-complete problems, is there any good reference dealing with the VC dimension of such problems ? 

In Galit Shmueli's "To Explain or Predict," https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict, on pages 5 and 6, there is a reference to Hastie, Tibshirani, and Freedman(2009), for statistical learning, which breaks expected square of the prediction error into the two parts of a variance of a prediction error and the square of the bias due to model misspecification.  (Variance - bias tradeoff is discussed in Hastie, et.al. and other sources.)   

An example of another kind of variance bias tradeoff that comes to mind would be the use of cutoff or quasi-cutoff sampling for highly skewed establishment surveys using model-based estimation (i.e., prediction from regression in such a cross-sectional survey of a finite population).  The much smaller variance obtained is partially  traded for a higher bias applied to small members of the population that should not be very much of the population totals (as may be studied by cross validation and other means).  Thus some model misspecification will often not be crucial, especially if applied to carefully grouped (stratified) data.

[Note that if a BLUE (best linear unbiased estimator) is considered desirable, it is the estimator with the best variance, so bias must be considered under control, or you have to do something about it.] 

Other means to tradeoff variance and bias seem apparent:  General examples include various small area estimation (SAE) methods.  - 

Shrinkage estimators tradeoff increased bias for lower variance. 

Are there other general categories of applications that come to mind? 

Do you have any specific applications that you might share? 

Perhaps you may have a paper on ResearchGate that relates to this.

Any example of any kind of bias variance tradeoff would be of possible interest.

Thank you.

I am looking for the materials where applications of methods in statistical learning in hydrology is explained.

I am interested in studying students reasoning while learning a measure of variation and how making connections to the measures of center can improve retention. How is variation, more specifically the Mean Absolute Deviation (MAD) taught in sixth grade, and has there been any research that might be related?

I don't yet have a clear hypothesis, but a muddy one might be  that a group provided with extended relational instruction (where connections are made between a measure of center and the MAD by both computing the MAD as a percentage of the measure of center as well as computing an expected range of values) will perform better on posttest and retention evaluation assessments for center, variation and proportional reasoning than another group (with the same teacher) who are provided with computational reinforcement for their additional instruction time. 

It seems most instructional material I have seen (NC Mathematics "How MAD are you and LearnZillion.com for example) has the student compute the MAD, but not connect or relate it to to the center by computing an expected value range or expressing it as a percentage.

Thanks in advance for your assistance!!! 

I was wondering if anyone has any good suggestions for solving the filtering problem when you have a hidden Markov model where the hidden chain x_k has a very large state space? By very large I mean that the exact solution (http://en.wikipedia.org/wiki/Forward_algorithm) becomes too computationally demanding.

My application is basically a discrete spatio-temporal model where for each time instance the transition probability is a Markov random field with nearest neighbour interaction.

The aim of probability predication is to predict pages to be dirtied in the next iteration by taking into account its previous history using probability table in virtual machine environment. Can we consider this problem analogous to time series analysis? I am also interested to know whether statistical learning is already used by someone or not? Please indicate.

I'm not a statistician. Just an interested MD. So, please, suggest somethitng relatively understandable. WinBUGS, e.g., is out of question. It has to have GUI, not only a command line. I have some expirience in Object Pascal and Java but not much. I'd appreciate any advise for beginner. I'm planning to start with observational longitudinal data (register and survey) and, maybe later, move towards network meta-analysis.

Bayesian statistics has been applied to a language change modeling (ex Niyogi & Berwick 1995, Griffiths & Kalish 2007 etc). I am looking, however, for any research that implemented Bayesian statistics to actual linguistic data, ex. a diachronic or synchronic linguistic variation. I would greatly appreciate any suggestion or advice, as I am hoping to use (hierarchical-)Bayesian model on historical categorical data in my thesis. Thank you!

Price-elasticity models do not fit here (since they need previous/historic data with price changes to 'learn' the effect).

We have sales-data for different items (with no price-changes till now). Business owners are thinking of changing the prices for the first time, and would like to estimate the customer reaction. (Customers are not tracked, anonymous and opportunistic).

Any pointers on the right approach (R package) ?

In K-mean clustering, every data point is being clustered. The data points which are supposed to be treated as noise are also considered in clusters. Is there any possible way to reduce such noise or a hybrid of K-mean clustering?

\begin{equation*} \quad min_{M,C_1,C_2}\frac{1}{N_T N_L} \sum_{\substack{ 1\le i \le N_T\\ j s.t. f_l(z_i,z_j)=1 m}}V(M,z_i,z_j)+\beta\|M\|_F^2 \end{equation*} \begin{equation*} \qquad \space \qquad \quad s.t. \qquad V(M,z_i,z_j) = \begin{cases} [C_1-d_M(x_i,x_j)]_+ & \text{if } l_i \neq l_j \\ [d_M(x_i,x_j)-C_2]_+ &\text{if } l_i = l_j \end{cases} ,\qquad \end{equation*}

\begin{equation*} \quad , \qquad \end{equation*} \begin{equation*} \qquad \qquad \quad \qquad M_{i,j}\geq 0, \qquad 0 \leq i,j \leq dim(M) \end{equation*}

I am looking for a classifier that will give us an error bound (expected performance) on test data. Also, we should not assume the data is independent and identically distributed) or features have any particular distribution. Any suggestion is appreciated.

How can final set of features be selected from multiple rank lists obtained by different ranking method?

What are the parameters (parameters of the model) that may influence a Bayesian neural network?

Khinchine's inequality gives me an upper bound on the r.h.s. of (sum_i x_i^2)^(1/2) but I found nothing about the stronger equality being true though the numerics suggest it.

I am wondering whether deep learning can give better results than boosted models.

Related to sequence learning and reactivation

In research, I have a set of random forests which are generated from a given set of datasets. Now I would like to calculate the description size (based on the MDL method proposed by Quinlan) of each of these random forests. Do you have any idea how I can calculate it?

I have four variables which are correlated to each other, thus should I do partial correlation to find correlation between any two random variables with other two control variables?

Since random forest includes a bunch of random decision trees, it is not clear when we say forest size, it can be :

1) number of bits it takes

2) number of decision trees included in forest

3) accuracy

4) execution time

5) a manifold of all of above terms

6) etc.

What is the most important and what is the best?