New answers tagged machine-learning
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ML is an extremely broad subject but generally it can be understood broadly as follows
you formalize the problem
you identify the domain of the problem
you identify candidate models to solve the problem
you evaluate the candidate models with data subsets
you select a model and try to fit your data
you deploy the model
You can think of it as a(n ...
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You can apply transfer learning. Leverage one of the existing datasets and deep learning networks that can classify faces e.g. celebrities.
Add/remove layers on top of the feature extraction layers and use your small data set. Provided that the base dataset / network is large and rich enough you should be able to apply it to your dataset.
See https://...
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Given normalized top $k$ eigenvectors $v_1,\ldots,v_k$, you send a point $x$ to the tuple $(\langle x,v_1 \rangle, \ldots, \langle x,v_k \rangle)$.
Alternatively, you put the eigenvectors as rows in a matrix $M$, and you map the column vector $x$ to $Mx$ (this is exactly the same thing as above).
Multiplying vectors is an operation that doesn't have much ...
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In fact, the VC dimension is 3.
To show this, we need to show that there is a set of 3 points which is shattered, and that no set of 4 points is shattered.
All sets of 3 points behave the same, but for definiteness let us choose three points $x,y,z$ which form the corners of an equilateral triangle. By symmetry, there are only 4 cases to consider:
$\...
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Let us prove the following general result:
Let $\mathcal F$ be a class of functions from $\mathcal X$ to $\{0,1\}$. If $\mathcal F$ has VC dimension $d$ then $|\mathcal F| \geq 2^d$.
Indeed, if $\mathcal F$ has VC dimension $d$ then $\mathcal F$ shatters some set $S \subseteq \mathcal X$ of size $d$. This means that for any function $\phi\colon S \to \{0,...
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Håstad gave an even better example in his paper On the Size of Weights for Threshold Gates, which requires super exponential weights.
A simple example which requires exponential weights is the function $\sum_i 2^i (x_i - y_i) \geq 0$ or variants.
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