4

Recall that the final hypothesis after $T$ rounds is $h_T(x)=sign\left(\sum\limits_{i=1}^T \alpha_t h_t(x)\right)$, i.e. $\alpha_t$ is the weight of $h_t$ in $h_T$. If $\epsilon_t$ is high (near one) you want to answer the opposite of $h_t$, so you want $\alpha_t$ to be negative and very large in absolute value. If on the other hand $\epsilon_t$ is very low ...


3

Since each $x$ is uniformly chosen, the probability of having a certain value at the $i$'th spot is independent of the probability of finding some other certain value in the $j$'th spot. You showed this already, but notice it means that you dont need the inclusion-exclusion principle, and instead the probability will just be the probability of the complement,...


3

The notation $A^T$ stands for the transpose of a matrix. It is not specific to machine learning, but rather standard notation in linear algebra. Other notations are sometimes used, for example $A'$. A related operation is the adjoint $A^*$. The transpose and adjoint are equal for real matrices.


2

AI is probably not the best tool for this job. Several classical techniques in survey design include: Consistency check: ask the same question in several ways, spread out across the survey, and check if they've answered consistently. Open-ended questions: ask an open-ended question, see if they write nonsense or the bare minimum. Attention check ...


2

Complexity theory is mostly interested in decision problems and in optimization problems, and your problem belongs to neither class. Complexity theory is also interested in other resources, such as communication, but at the cost of neglecting computational complexity. Apart from not fitting the mold of problems typically considered in complexity theory, your ...


2

Your analysis appears fine, it remains to apply the binomial formula to compute your sum. $\sum\limits_{i=1}^N (-1)^{i-1} {N\choose i}\frac{1}{2^{mi}}=1-\sum\limits_{i=0}^{N}(-1)^i {N\choose i}\frac{1}{2^{mi}}=1-\left(1-\frac{1}{2^m}\right)^N\ge 1-e^{-N/2^m}\ge\delta$, Where the last inequality holds for $N\ge 2^m\log\frac{1}{1-\delta}$.


2

I think a natural approach would be to constrain the coefficient of adjO_T2 to be the negation of the coefficient of adjO_T1, the coefficient for adjD_T2 to be the negation of the coefficient for adjD_t1, etc. Then, you could learn a logistic regression model subject to that constraint. This could be implemented in practice by having only the coefficients ...


1

Let $x_1,...,x_N$ denote the elements of $\mathcal{X}$ and consider the marginal distributions $D_\mathcal{X}=(p_1,...,p_N)$ and $G_\mathcal{X}=(q_1,...,q_N)$. Recall that $p_i>0$ implies that $q_i>0$, hence the ratio $R=\max_i\frac{p_i}{q_i}$ is well defined. Also denote the output of the algorithm on a sample set $S$ by $h_S$, then: \begin{align*} ...


1

Let’s say your self driving car is supposed to do the following steps in a loop: Read all the sensors. Calculate optimum pressure on accelerator and brakes Calculate optimum angle for steering wheel Set the optimum pressure and angle. Now if the calculation takes too long then it is no good, your car will crash before the calculation finishes. So instead ...


1

This is not an easy task. There is no simple answer; you could do something crude that might give mediocre results, or you could put a lot of effort into it; and it's not obvious to me what will work best. One possible simple approach is to map each word (except for a few stopwords) to an encoding, using a standard word embedding (e.g., word2vec), average ...


1

It is used for: Image analysis, and specially face recognition and search photos library. Language detection, text recognition and analysis ( to identify concepts in a text ). Used for advanced search in text Speech recognition Sound analysis, for efficient filtering and removal of noise in conversations and sound recognition ( Be able to differentiate ...


1

This is murky indeed. I can't say I agree with the distinctions mentioned about parameterization. I think there are parametric and non-parametric examples of both. My 2 cents: a major distinction is the direction of causality in the system. In ML the "real-world" direction of causality can go in either direction x-to-y or y-to-x, but the model ...


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