Questions tagged [theory]
Theory relates to theoretical questions regarding data science and machine learning.
48
questions
0
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2answers
41 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 ...
2
votes
1answer
28 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 ...
3
votes
1answer
47 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 ...
2
votes
2answers
25 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 ...
0
votes
1answer
18 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 a has an effect on B.
I also believe that A and B both have an effect on C.
I don't think C has an effect on ...
0
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0answers
8 views
How to introduce a parameter for measuring change in data over time
In my project, I need to introduce a measure for 'movement' using a 3axis accelerometer (ADXL345). As sketched below:
I thought about introducing some micro-changes, i.e. absolute change in ...
3
votes
1answer
180 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 ...
0
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1answer
33 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 ...
1
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1answer
24 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 "...
1
vote
2answers
86 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)...
1
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1answer
22 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 ...
0
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0answers
13 views
Skipgram model theory confusion
In the output layer of a skipgram model, there are $|\text{Context}|*|\text{Vocab}|$ values. And for each context word, the values are basically the dot product of the input word representation and ...
0
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0answers
17 views
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 $y_i$ ...
0
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0answers
11 views
Theoretically Speaking, How Do Squeeze-and-Excitation Blocks Help?
A SE block works by assigning a weight to each channel, contrary to a vanilla filter, which gives equal importance to all channels. My question is, theoretically speaking, shouldn't a regular filter ...
0
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0answers
16 views
A causal story is not causality either
I am pursuing a course on Edx on data analysis for Social Sciences. Actually I am stuck on this assertion of the teacher Mrs. E. Duflo which states:
Correlation is not causality.
A causal story is ...
2
votes
0answers
139 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 ...
1
vote
1answer
79 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 ...
1
vote
1answer
451 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 ...
0
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1answer
42 views
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 ...
1
vote
1answer
33 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 ...
1
vote
2answers
206 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'...
0
votes
1answer
30 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 ...
2
votes
1answer
28 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 ...
2
votes
1answer
45 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 ...
0
votes
1answer
80 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
...
2
votes
1answer
44 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 ...
3
votes
1answer
32 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, ...
4
votes
1answer
106 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):
$$\...
2
votes
1answer
40 views
An ambiguity in SVM equations about misclassified data
I have encountered an ambiguity in SVM equations.
As is stated in Chris Bishop's machine learning book, the optimization goal in SVM is to maximize this function:
$$C\sum\limits_{n = 1}^N {{\xi _n}} ...
2
votes
1answer
73 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. ...
1
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0answers
39 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 ...
0
votes
2answers
94 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 ...
0
votes
1answer
44 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 ...
0
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1answer
87 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 ...
2
votes
0answers
145 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 $error_D \leq \epsilon$, ...
1
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0answers
25 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 ...
5
votes
1answer
267 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. ...
1
vote
0answers
92 views
How do you calculate the information capacity of a neural network?
Let's say I wanted to train a neural network to teach it the rules in a decision tree, so I generated a dataset by feeding arrays of random numbers into the pre-trained decision tree, and then used ...
4
votes
0answers
79 views
Learning a logical function with a 2 layer BDN network - manual weight setting rule question?
So I am trying to construct a 2-layer network of binary decision neurons as proposed by McCullough and Pitts (1943) to learn a logical function (a composition of AND's and OR's) such as:
$((\neg x_1\...
0
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1answer
37 views
Situations where advanced theoretical knowledge of ML helped solve a real world problem?
I've invested lot of time trying to understand the theoretical aspects of Deep Learning and Neural Networks - but I'm now questioning whether it is worth it or not, given that I am someone who works ...
1
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0answers
32 views
Why study properties with infinitesimal change?
I read about analysis on local properties of neural networks. Some of them study the impact of "infinitesimal" change to an input. Like in Percy Liang's paper Understanding Black-box Predictions via ...
1
vote
1answer
83 views
What's the math for real world back-propagation?
Considering a simple ANN:
$$x \rightarrow
f=(U_{m\times n}x^T)^T \rightarrow
g = g(f) \rightarrow
h = (V_{p \times m}g^T)^T \rightarrow
L = L(h,y)
$$
where $x\in\mathbb{R}^n$, $U$ and $V$ are ...
3
votes
1answer
99 views
Is there a name for a scale which mixes ordinal and nominal?
The textbooks I have differentiate between nominal, ordinal, interval and ratio scales. The ordinal scale is quite popular in the wild, used for basically all subjective data, and also for dividing ...
1
vote
1answer
198 views
Softmax function forms
The constraint that the n outputs must sum to $1$ means that only $n−1$
parameters are necessary; the probability of the $n^{th}$ value may be
obtained by subtracting the first $n−1$ probabilities ...
13
votes
8answers
1k views
Difference between machine learning and artificial intelligence
Is there any difference between machine learning and artificial intelligence? Or do these terms refer to the same thing?
8
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1answer
1k views
Deriving backpropagation equations “natively” in tensor form
Image shows a typical layer somewhere in a feed forward network:
$a_i^{(k)}$ is the activation value of the $i^{th}$ neuron in the $k^{th}$ layer.
$W_{ij}^{(k)}$ is the weight connecting $i^{th}$ ...
1
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0answers
182 views
Global vs. local bias-variance tradeoff
In the standard example of decomposing the MSE into Bias, Variance and Irreducible error: $$MSE(x) = \left(\mathbb{E}[\hat{f}(x)] - f(x) \right)^2 + \mathbb{E}\left[\left(\hat{f}(x) - f(x)\right)^2\...
1
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3answers
1k views
What would be the best way to impute data?
Other than just filling in with the mean of a feature, what other methods are there which can work well? I am trying to decide whether or not to use a denoising-autoencoder or just impute with the ...
