Intereting Posts

Asymptotic expansion of a function $\frac{4}{\sqrt \pi} \int_0^\infty \frac{x^2}{1 + z^{-1} e^{x^2}}dx$
On a necessary and sufficient condition for $\sum_{k\in\mathbb{Z}}a_k=L$ ($a_k\in\mathbb{C}$)
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
What is the product of all nonzero, finite cardinals?
Derivation of the formula for Ordinary Least Squares Linear Regression
Is it a good approach to heavily depend on visualization to learn math?
Extending an automorphism to the integral closure
composition of certain covering maps
A question on conditional expectation leading to zero covariance and vice versa
Detail in Conditional expectation on more than one random variable
Is there a name for the group of complex matrices with unimodular determinant?
Calculate $\int_{0}^{\pi} \frac{x}{a-\sin{x}}dx , \quad a>1$
How to prove conformal self map of punctured disk ${0<|z|<1}$ is rotation
Rigorous Proof?: Proving Cauchy Criterion of Integrals
Is there a distributive law for ideals?

In my machine learning class I have been provided a weight vector that has the property that it is **generously feasible** ?

Formally, what does **generously feasible** mean? I can’t seem to find a definition?

- Unbiased estimator of a uniform distribution
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- Geometric distribution with unequal probabilities for trials
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- Why is there not a simpler way to calculate the standard deviation?

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- Maximum of the Variance Function for Given Set of Bounded Numbers
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- Recommended Reading on Regression Analysis?
- What is the difference between probability and statistics?
- On Martingale betting system
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- What is the importance of functions of class $C^k$?
- Is the notion of “affineness” more general than “linearity”, or vice versa?
- Unbiased estimator of the variance with known population size

If the weight vector in the current iteration is in the region between the hyperplane and the magnitude of input vector, i.e. $\vec{w^t_x} \: \epsilon \: [ \langle \vec{w_{x}},\vec{x} \rangle , |\vec{x}| ]$, where $\langle \vec{w_{x}},\vec{x} \rangle$ is the hyperplane, then, since the perceptron adds $\vec{x}$ or $-\vec{x}$ to the weights each iteration, the weight vector will oscillate around the hyperplane. Hence for the algorithm to terminate with a solution, it should be allowed to accept a solution in this feasible space, hence called the “generously feasible” space.

So consider “generously feasible” weight vectors that lie within the feasible region by a margin at least as great as the length of the input vector that defines each constraint plane.

Every time the perceptron makes a mistake, the squared distance to all of these generously feasible weight vectors is always decreased by at least the squared length of the update vector.

- Chatting about mathematics (with real-time LaTeX rendering)
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- $\int_C \frac{\log z}{z-z_0} dz$ – Cauchy theorem with $z_0$ outside the interior of $\gamma$
- For a given positive integer $n>1$ , how to find all positive integers $s,t$ such that $n^s-(n-1)^t=1$ ?
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- Cardinality of $GL_n(K)$ when $K$ is finite
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- differentiablility over open intervals
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- If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.