Questions tagged [theory]
Theory relates to theoretical questions regarding data science and machine learning.
51
questions
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28 views
Can XGBoost support vector outputs?
I am interested in fitting data (regression rather than classification) with individual targets which are vectors via an XGBoost type model. However, currently Python's xgboost.XGBRegressor model only ...
0
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0answers
23 views
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 ...
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0answers
14 views
End-to-end machine learning project processes
I've read a book chapter that walks you through all the steps involved in an end-to-end machine learning project. After doing all the practical exercises I'm still not quite sure that my way of ...
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1answer
14 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 ...
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3answers
62 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
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1answer
33 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
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1answer
53 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
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2answers
26 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
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1answer
31 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 ...
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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
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1answer
229 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 ...
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1answer
36 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 ...
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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 "...
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2answers
134 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 ...
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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 ...
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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 $y_i$ ...
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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 ...
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0answers
164 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 ...
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1answer
88 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
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1answer
750 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
45 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 ...
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1answer
43 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 ...
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2answers
234 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'...
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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
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1answer
30 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
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1answer
48 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 ...
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1answer
81 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
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1answer
48 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
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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
110 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):
$$\...
2
votes
1answer
41 views
An ambiguity in SVM equations about misclassified data
I have encountered an ambiguity in SVM equations.
As is stated in Chris Bishop's machine learning book, the optimization goal in SVM is to maximize this function:
$$C\sum\limits_{n = 1}^N {{\xi _n}} ...
2
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1answer
74 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. ...
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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
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2answers
95 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
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1answer
47 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
89 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
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0answers
146 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 $error_D \leq \epsilon$, ...
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0answers
26 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 ...
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1answer
287 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. ...
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0answers
95 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
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0answers
80 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
38 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 ...
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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
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1answer
86 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
101 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
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1answer
200 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
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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 $i^{th}$ ...
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0answers
183 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\...
