Questions tagged [math]

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16 views

Can continuous dataset have negative values? [closed]

As in the description, I want to choose continuos dataset with temperatures and the minimun value is -40 and maximum is 51. Is that OK? Can we have negative values in continuous distribution?
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6 views

Static and Dynamic neural networks process

Neural networks can be classified into static (convention feedforward networks) and dynamic categories (RNN, LSTMs). ...
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0answers
33 views

Transitioning from Math PhD to ML research [closed]

I am currently a Math PhD about to defend in January. I work in a field in functional analysis that uses a lot of measure theory (but no stats). I have been considering transitioning careers since I ...
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0answers
25 views

Convergence speed of perceptron algorithm

I was reading the convergence proof for the perceptron algorithm. It says under the assumption that there are some $R$, $\theta^*$ with $|\theta^*| = 1$ and $\gamma > 0$, such that $y_t(x_t\cdot \...
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13 views

Is this interpretation of spectral normalisation mathematically correct?

Hello everyone, this is my first post. I was thinking about the mathematical interpretation for spectral normalization in neural networks the other day, and I came up with an explanation that feels ...
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1answer
34 views

SVM hyperplane margin

so that $H_0$ is equidistant from $H_1$ and $H_2$. However, here the variable $\delta$ is not necessary. So we can set $\delta=1$ to simplify the problem. $$w\cdot x+b=1 $$ and $$w\...
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2answers
44 views

Solving Bayes Theorem equation -> I can't calculate proper result

I am solving questions for an edx course on Machine Learning. One particular question is giving me a problem: Assume a patient comes into the doctor’s office to test whether they have a particular ...
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1answer
77 views

Understanding REINFORCE loss

The loss used in REINFORCE algorithm is confusing me. From Pytorch documentation : loss = -m.log_prob(action) * reward We want to minimize this loss. If a ...
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1answer
51 views

Skew and Kurtosis are so similar?

I've been taking the histogram of the optical flow in videos and plotting the kurtosis and skewness of each frame. At the end of the video, I noticed that the skewness and kurtosis follow each other - ...
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2answers
53 views

How to learn certain Maths to understand machine Learning papers?

I have done the deeplearning.ai course on deep learning. But I cannot Understand equations like minGmaxDV(D,G)=Ex∼pdata(x)[logD(x)]+Ez∼pz(z)[log(1−D(G(z)))] ...
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1answer
18 views

Choose points to maximize volume of convex hull

Suppose I have N points (labeled 1, 2, ..., k, ..., N) in D dimensions. I'd like to choose ...
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0answers
52 views

How to determine percent contribution to classification in logistic regression?

I'm trying to understand the contribution of each feature towards a specific classification. Let's say I have clients as my data and their features are income, debt and age. We're trying to predict ...
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1answer
71 views

bias variance decomposition for classification problem

It is given that: MSE = bias$^2$ + variance I can see the mathematical relationship between MSE, bias, and variance. However, how do we understand the mathematical intuition of bias and variance for ...
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0answers
21 views

How to create an autograd library from scratch like pytorch?

I am trying to implement a deep learning library from scratch. Most common DL framework uses autograd. Unfortunately, I haven't seen a lot of resources on how to create one autograd library. Is there ...
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0answers
18 views

How to add extra constraints to an equation?

Background: I have an equation which looks like as follows: $W \times P = R$ $\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \\...
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2answers
52 views

Neural networks, optimization math intuition

When I look into the following partial derivative, I see it as being the key element of any optimization algorithm out there. Correct me if I'm wrong, but this gets us the slope of the loss function, ...
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1answer
122 views

Estimating the value of $\pi$ with a Monte Carlo dartboard: $<$ or $\leq$?

I'm trying to figure out which is the proper way to estimate $\pi$ using the Monte Carlo method randomly distributing points in a square that also contains an inscribed circle. Some sources say to ...
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0answers
7 views

Confidence vs. Count in association rule mining: which one is better?

I am writing a program that mines association rules from a large data set. I have an array of association rules, and I have to decide which ones are more representative of the patterns I am studying. ...
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1answer
55 views

What is the range of values of the expected percentile ranking?

I'm currently reading Hu, Koren, Volinsky: Collaborative Filtering for Implicit Feedback Datasets One thing that confuses me is the "expected percentile ranking", an function the authors define to ...
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1answer
399 views

What are CRF (Conditional Random Field)

Looking for language modeling, I have been finding CRF in a lot of places which is but looking online for the same isn't actually helping me a lot. I referred Edwin Chen's blog and Ravish Chawala's ...
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1answer
36 views

Meaning of this notion in 0-1 loss?

I am reading a paper and encountered this notion: $$1_{\{Y=1\}}$$ To me it seems to be the expression as below, but I am not entirely sure and I don't think the author explictly explained it: <...
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1answer
15 views

Looking for help calculating a probability formula

How do I put this into a calculator or a excel spreadsheet formula. I have never done this math before, but I want to figure it out.
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2answers
25 views

compare log and division of numbers

What is the difference between (a) taking the logarithm of a set of numbers (b) dividing the set of numbers by an integer. Both appear to reduce the scale of set of numbers, so can they be used ...
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1answer
13 views

What is the first tool to learn start your your data science projects? [closed]

What is the first tool to learn start your your data science projects?
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1answer
39 views

How can positional encodings including a sine operation be linearly transformable for any offset?

In the paper "Attention is all you need" the authors add a positional encoding to each token in the sequence (section 3.5). The following encoding is chosen: $ PE(pos, 2dim) = sin(pos / 10000 ^ {2dim/...
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1answer
192 views

Comparison between addition and multiplication function in deep neural network?

I designed a specific Convolution Neural Network to study in the area of image processing. The network has a part that there are two tensors which have to be transformed into a tensor in order to be ...
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1answer
43 views

What is the difference between parameters & cooficients in Machine learning?

are both terms interchangeable? I'm kinda new to machine learning field and very confused about these terms in machine learning perspective.
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0answers
26 views

Continuous Function Input

If a continuous function has trouble differentiating between small close numbers (i.e. 0.1 and 0.001) why can we train and learn such small numbers in something like word2vec?
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1answer
33 views

Which algorithm is perfect to determine best fit analyst based on multiple factors?

Assume I have a team of 200 analyst who work on different IT tickets. I want a better ticket assignment system which considers multiple factors before ticket assignment. Outstanding Ticket with each ...
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0answers
10 views

Should we invest more in exploration (as opposed to exploitation) when the distribution is fat-tailed in contrast to a bell-curve?

Not sure if this falls under data science but here it goes: In the exploration/exploitation trade-off (deliberation vs commitment to one choice), should we invest more in exploration when the ...
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0answers
28 views

What are the introductory mathematics courses that are most pertinent to machine learning?

To provide more context to this question, I have found the following list of courses in order to learn calculus: Course | 18.01.1x | edX Course | 18.01.2x | edX Course | 18.01.3x | edX I also have ...
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1answer
52 views

Do we need to add the sigmoid derivative term in the final layer's error value?

I have been studying professor Andrew Ng's Machine Learning course on Coursera. Currently, I am trying to prove the formulas for backpropagation, which is mentioned in Week 5 (in this document). ...
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2answers
40 views

How to tell if the “clusters” I see in my pair plots are statistically significant or occurring by random chance?

I have a data set with one row per subject. Some variables include laboratory parameters for blood chemistry, hematology, etc. I also have some flag variables: any = 1 if the subject experienced an ...
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2answers
175 views

word2vec - log in the objective softmax function

I'm reading a TensorFlow tutorial on Word2Vec models and got confused with the objective function. The base softmax function is the following: $P(w_t|h) = softmax(score(w_t, h) = \frac{exp[score(...
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2answers
501 views

Can a single-layer ANN get XOR wrong?

I'm still pretty new to artificial neural networks. While I've played around with TensorFlow, I'm now trying to get the basics straight. Since I've stumbled upon a course which explains how to ...
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2answers
25 views

Are euclidian vectors and unit vectors same thing? [closed]

Consider this statement : Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R3. Consider the vectors e1 = (1,0,0), e2 = (0,1,0) and e3 = (0,0,1). Then any ...
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1answer
72 views

Finding orthogonal input patterns associated with logistic function output

I've been given this problem but cannot seem to get an analytical solution. I've tried satisfying the logistic function with several vectors but have difficulty finding ones which are also orthogonal. ...
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1answer
2k views

Knn and euclidean distance

I'm studying the knn classification algorithm. Why can the euclidean distance be considered a nice measure of affinity between examples ? In one dimension (1 attribute) this seems correct, but if I ...
3
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1answer
76 views

How to quantify the numerical influence of categorical variables?

I have trained a simple neural net, to make predictions based on three inputs. For examples sake lets say I m trying to work out "how many days does it take to complete an accademic study", where the ...
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1answer
23 views

What does the term “proportional to” mean in Bayes Equation?

I don't have a background in maths so I sometimes get confused by basic definitions. Let's for instance consider Bayes Theorem in Bayes Data Analysis: $P(\theta|\textbf{y}) \propto P(\theta) P(\...
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3answers
3k views

What does it mean when we say most of the points in a hypercube are at the boundary?

If I have a 50 dimensional hypercube. And I define it's boundary by $0<x_j<0.05$ or $0.95<x_j<1$ where $x_j$ is dimension of the hypercube. Then calculating the proportion of points on the ...
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1answer
6k views

Recreating the sum symbol using python

I am currently reading a white paper relating to Expectation-Maximisation (EM) and would like to encode a formula so I can play with it in order to help my understanding. The formula in question is a ...
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5answers
3k views

Beginner math books for Machine Learning

I'm a Computer Science engineer with no background in statistics or advanced math. I'm studying the book Python Machine Learning by Raschka and Mirjalili, but when I tried to understand the math of ...