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Questions tagged [theory]

Theory relates to theoretical questions regarding data science and machine learning.

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Сan we say that the regression problem is essentially a classification problem with an infinite number of classes?

I'm a newcomer to machine learning and currently diving into supervised learning methods. I've already grasped the theoretical basics of classification tasks and have just started exploring regression....
SuperciliousMe's user avatar
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16 views

Reinforcement Learning: Formally, does an exponentially decaying epsilon satisfy GLIE?

I am aware that exponentially decaying exploration constants (epsilon) are used practically. Formally, though, do they satisfy the GLIE condition? Specifically, relating this to the Borel-Cantelli ...
jeremy.ebg's user avatar
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28 views

Check the validity of the distribution in the proof of No-Free-Lunch Theorem

I'm reading the proof of No-Free-Lunch Theorem (quoted at the end of this question) in Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, p.37, the author wrote: ...
Tran Khanh's user avatar
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Why do we use Gradient Descent for Norm Batch since the function has only 2 parameters?

So here is the formula for Z sedile ( gamma * Z + Beta). Since it's a function of 2 parameters why there is still stated in courses that we need to compute gradient descent to find the slope ? Since ...
Lazu Razvan's user avatar
1 vote
1 answer
61 views

Where does AI/ML theories come into play when nowadays the AI libraries already so powerful?

I've read up posts so-call for beginning ML, claiming you need linear algebra, statistics, complicated optimization to just getting start in ML/AI. And on top of these, there comes the ML/AI ...
Student's user avatar
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Are there any established approaches for dealing with a Degenerate Feedback Loop?

Scenario: I develop a model which forecasts the likely sales success of a particular enquiry based on outcomes of past similar enquiries. I then assign this likelihood score to new enquiries when they ...
Ian's user avatar
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1 answer
214 views

How to scale a subset of data with respect to the entire dataset

I am developing a financial time-series prediction model using sklearn using StandardScaler for scaling purposes. I train a model, and then use the model regularly ...
functorial's user avatar
2 votes
0 answers
57 views

Minor error in Ian Goodfellow's GAN optimality proof

I've been thinking of a part of the proof of the optimality of GANs from the original paper, and I can't manage to solve what seems to be an error. The paper states that the maximum of the function $y ...
J. P. C.'s user avatar
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1 answer
38 views

How do we derive our loss function from the gradient objective?

I've been dwelling through RL theory and practice and one particular part I find hard to properly understand is the relation between the practical loss function and ...
Alex Ramalho's user avatar
2 votes
0 answers
10 views

Learning the Average of a 0/1 Dependent Variable

uppose I have a matrix 𝑋 and a dependent vector 𝑦 whose entries are each in {0,1} dependent on the corresponding row of 𝑋 Given this dataset, I'd like to learn a model, so that given some other ...
Ami Tavory's user avatar
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Creating a map between N images and N labels using CNN

I have seen classification CNNs that train with numerous images for a subset of labels (i.e. Number of images >> Number of labels), however, is it still possible to use CNNs when the number of ...
Akash's user avatar
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3 answers
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Time series test data dilema

I’m trying to build a model to predict the amount of sales of a product for the next few days This question is about whether or not I should use the tail of the serie as the test set and train models ...
drumkey's user avatar
1 vote
1 answer
109 views

Proof of GOSS algorithm in lightGBM paper

In the LightGBM paper the authors make use of a newly developed sampling method GOSS to reduce the number of data instances needed for finding the best split of a ...
HannesZ's user avatar
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How to use the eval set in catboost appropriately?

Let's say you have a dataset, and you split it into 80% training and 20% testing. Naturally, you want to find the optimal hyperparameters for your model, so with the training set, you plan to do cross ...
user125720's user avatar
1 vote
1 answer
19 views

Would all classification models perform similarly in a theoretical and ideal scenario?

Imagine that we count on infinite computation power, an infinite amount of data and we have an infinite amount of time to wait for a model to learn. In such a scenario, we want to have some data ...
Tendero's user avatar
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3 answers
180 views

Which neural network is better?

MNIST dataset with 60 000 training samples and 10 000 test samples. Neural network #1. Accuracy on the training set: 99.53%. Accuracy on the test set: 99.31%. Neural network #2. Accuracy on the ...
user51515151's user avatar
2 votes
3 answers
99 views

Why do the performance of DL models increase with the volume of data while that of ML models will flat out or even decrease?

I have read some articles and realized that many of them cited, for example, DLis better for large amount of data than ML. Typically: The performance of machine learning algorithms decreases as the ...
Lam TRINH Thanh's user avatar
3 votes
1 answer
297 views

Given M binary variables and R samples, what is the maximum number of leaves in a decision tree?

Given M binary variables and R samples, what is the maximum number of leaves in a decision tree? My first assumption was that the worst case would be a leaf for each sample, thus R leaves maximum. Am ...
yaminlee's user avatar
2 votes
2 answers
140 views

How to input a list into my model and not have it care about order

I'm trying to predict a list of numbers, e.g: [23,55,198,200,64] The data I have includes multiple things, along with: The numbers from the previous run (These ...
SirAchesis's user avatar
1 vote
1 answer
542 views

Use of multiple models vs training a single model for multiple outputs

So let's say I have data with numerical variables A, B and C. I believe that the value of <...
SirAchesis's user avatar
3 votes
1 answer
390 views

What is Inductive bias?

Bias in a neural network is an additional neuron to be fired i.e let $y=a+bx$ where $a$ is a bias term. Do we have any difference between bias and inductive bias? How Inductive bias is helpful in ...
SS Varshini's user avatar
0 votes
1 answer
322 views

Multiple solutions with same minima in MLP with same weights

I came across an excercise on deep learning from here. It goes as follows: Consider a simple MLP with a single hidden layer of $d$ dimensions in the hidden layer and a single output. Show that for any ...
scaraven's user avatar
1 vote
1 answer
34 views

Theoretical basis for neural network "effort"

I might be in danger of having my question closed as "not clear what I'm asking for," but here goes. Suppose we have a simple feedforward network. It has a few layers, each layer has a "...
Elliot Way's user avatar
1 vote
2 answers
641 views

What is the opposite of baseline?

I have created a prediction model and on the one hand I have to compare it with other baseline models, and on the other hand, I have to compare it with the ideal approach (supported by additional data)...
joe_mind's user avatar
1 vote
1 answer
67 views

Are non-relu activations better for small/ dense datasets?

Building on the questions below, the only conclusion I could draw from the answers was that ReLu is less computationally expensive and better at sparsity. Why is ...
Kermit's user avatar
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0 answers
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Unbiased Predictions for all Distinct Training Subsets

Suppose I have a data set $\left(X_i \in \chi, y_i \in \zeta \right)$ where $X_i$ and $y_i$ correspond to instances and labels, and $\chi$ and $\zeta$ correspond to the space where $X_i$ and $y_i$ ...
Luke Polson's user avatar
2 votes
0 answers
250 views

How to get the maximum likelihood estimate of the categorical distribution parameters using Lagrange optimization?

Let's say our data is discrete-valued and belongs to one of $K$ classes. The underlying probability distribution is assumed to be a categorical/multinoulli distribution given as $p(\textbf{x}) = \...
Shashank Kumar's user avatar
2 votes
0 answers
382 views

Why does Jim Gray call "data-driven science" a new paradigm?

Wikipedia it says about data science: Turing award winner Jim Gray imagined data science as a "fourth paradigm" of science (empirical, theoretical, computational and now data-driven) and ...
Make42's user avatar
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1 vote
1 answer
186 views

Can a neural network be of variable depth?

It is very common for neural networks to be asymmetric about the x axis, that is, to have many more nuerons in the first few layers than in the last few layers. Common example: But can neural ...
stevec's user avatar
  • 211
1 vote
1 answer
4k views

What is an object detection problem with only one class called?

Object detection is defined as the problem in which a model needs to figure out the bounding boxes and the class for each object. A lot of ML solutions for object detection base around having "two ...
agupta231's user avatar
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1 answer
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Gradient for starting Backpropagation

I was reading this nice tutorial about Pytorch's basics: https://pytorch.org/tutorials/beginner/pytorch_with_examples.html In the first example (pure Numpy), the author starts the backward phase by ...
MadHatter's user avatar
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1 vote
1 answer
108 views

What is the best approach for send time optimization? [closed]

I could no find a lot information about how the companies doabout send time optimization, either for push notifications or email campaigs. having historical data about clicks and sends what would be ...
user9075222's user avatar
1 vote
2 answers
635 views

Is the search space of Hyperparameters Continuous or Discrete?

I am looking into hyper-parameter tunning and was curious about whether the search space is considered continuous or discrete? My understanding of both those cases: 1. Continuous would make it 'easier'...
loulours's user avatar
0 votes
1 answer
35 views

What is the name of this statistical interaction?

What is the name of the following statistical / informational interaction: given A, I know exactly what B is. given B, I know to some extent what A is. I'm not looking for a probability but rather ...
Skusku's user avatar
  • 105
2 votes
1 answer
37 views

Structuring experiment/training data with months in mind

We're using a whole year's data to predict a certain target variable.The model works like data - OneHot encoding the categorical variables - MinMaxScaler - PCA (to choose a subset of 2000 components ...
lte__'s user avatar
  • 1,320
2 votes
1 answer
118 views

Encoding correlation

I have rather theory-based question as I'm not that experienced in encoders, embeddings etc. Scientifically I'm mostly oriented around novel evolutionary model-based methods. Let's assume we have ...
Piotr Rarus's user avatar
3 votes
0 answers
2k views

Explanation of inductive bias of Candidate Elimination Algorithm

The definition of inductive bias says that The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs given inputs ...
JustABeginner's user avatar
0 votes
1 answer
122 views

Understanding LSTM Keras implementation

So I understand what LSTM units are. But I have trouble understanding the implementation / function in Keras framework. Let's say, I add a layer ...
Marie M.'s user avatar
2 votes
1 answer
66 views

Popular classification algorithms over time

In the book "Deep Learning with Python" by Francois Chollet (2018), in section 1.2.4 one can find: Decisions trees learned from data began to receive significant research interest in the ...
Ruben Kazumov's user avatar
3 votes
1 answer
43 views

Is it possible for a neural net to score as high as a different form of supervised learning?

I've been working with the Adult Census Income dataset from UCI http://archive.ics.uci.edu/ml/datasets/adult I've created two different models, one using a gradient boosted classifier with sklearn, ...
user avatar
4 votes
1 answer
148 views

A trick used in Rademacher complexity related Theorem

I am currently working on the proof of Theorem 3.1 in the book "Foundations of Machine Learning" (page 35, First edition), and there is a key trick used in the proof (equation 3.10 and 3.11): $$\...
learning machine's user avatar
2 votes
1 answer
52 views

An ambiguity in SVM equations about misclassified data

I have encountered an ambiguity in SVM equations. As is stated in Chris Bishop's machine learning book, the optimization goal in SVM is to maximize this function: $$C\sum\limits_{n = 1}^N {{\xi _n}} ...
pythinker's user avatar
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2 votes
1 answer
87 views

A question on realizable sample complexity

I came across the following exercise, and I just can't seem to crack it: Let $l$ be some loss function such that $l \leq 1$. Let $H$ be some hypothesis class, and let $A$ be a learning algorithm. ...
Nadav Schweiger's user avatar
1 vote
0 answers
58 views

What could cause validation set to consistently perform better than training?

I'm training a neural network with a very small dataset just to get things set up, before training on a much larger set. (I only have about 500 data points available to me at this time, with more ...
wheresmycookie's user avatar
0 votes
2 answers
127 views

Decentralized machine learning

Currently, to train a model, you need to collect a huge blob of data. Are there feasible concepts of decentralized machine learning? Like, feed the model somehow from isolated data sources, or merge ...
Open Food Broker's user avatar
0 votes
1 answer
67 views

What does it mean when someone says "Most of the data science algorithms are optimization problems"

I was trying to understand the Gradient Descent algorithm from this article and the author says Most of the data science algorithms are optimization problems I come from software engineering ...
Aravind R. Yarram's user avatar
0 votes
1 answer
112 views

What should be the requirement for training data in order to obtain a good regression model using neural network?

I have made a neural network regression model using the theory for the first time and would like to clarify some basic doubts, whose concrete answers I couldn't find yet. Data:- I have 3000 samples ...
Manish's user avatar
  • 103
2 votes
0 answers
157 views

Intuition behind Occam's Learner Algorithm using VC-Dimension

So I'm learning about Occam's Learning algorithm and PAC-Learning where for a given hypothesis space $H$, if we want to have a model/hypothesis $h$ that has an True error of $error_D \leq \epsilon$, ...
JoeIsh's user avatar
  • 101
1 vote
0 answers
32 views

Is the hypothesis space spanned by kernel evaluations on datapoints equivalent to the hypothesis space of linear functionals in the feature space?

when studying kernel methods a few years ago I got a bit confused with the concepts of feature space, hypothesis space and reproducing kernel Hilbert space. Recently, I thought a little about ...
Chrisu's user avatar
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5 votes
1 answer
511 views

Are all classifiers linear in some high dimensional space?

Of all possible classifiers (including SVMs, locally weighted regression, softmax regression, lots others I'm sure I don't know about, etc.), are they all linear in some high dimensional space? E.g. ...
sidrane's user avatar
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