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Tags

#bayes #programming #r #statistics

Question

In other words, the normalizer for the beta distribution is the [equation]

Answer

beta function \(B(a,b) = \int d\theta \space \theta^{a-1}(1-\theta)^{b-1}\)

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In other words, the normalizer for the beta distribution is the beta function \(B(a,b) = \int d\theta \space \theta^{a-1}(1-\theta)^{b-1}\)

Tags

#deeplearning #neuralnetworks

Question

Kullbac k-Leibler (KL) div ergence : [...] (3.50) In the case of discrete v ariables, it is the extra amount of information (measured in bits if we use the base 2 logarithm, (but in machine learning w e usually use nats and the natural logarithm) needed to send a message containing symbols drawn from probability distribution P , when w e use a co de that w as designed to minimize the length of messages dra wn from probabilit y distribution Q.

Answer

\(D_{KL}( P||Q) = E_{x\sim P} [log\frac{ P (x )}{ Q (x )}] = E_{x \sim P} [log P(x) - log Q(x)] \)

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Kullbac k-Leibler (KL) div ergence : \(D_{KL}( P||Q) = E_{x\sim P} = [log\frac{ P (x )}{ Q (x )}] = E_{x \sim P} [log P(x) - log Q(x)] \) (3.50) In the case of discrete v ariables, it is the extra amount of information (measured in bits if we use the base 2 logarithm, (but in machine learning w e usually use nats and the

#1 #2 #anki #byrokratian_ihannemalli #klassiset_koulukunnat #lk1

tehokkuus aiheutui siitä, että virkoihin valittiin niihin koulutuksen saaneita henkilöitä

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#am #am-lk1 #anki #ihmissuhdekoulukunta #johtamis-ja_markkinointiajattelun_kehittyminen

Hawthorne-tutkimuksilla oli käänteentekevä vaikutus organisaatioteorioille, tuotannon sosiologialle ja työn psykologialle. Niiden vaikutuksesta tutkijoiden mielenkiinto siirtyi rakenteiden yksipuolisesta tarkastelusta sosiaalisten järjestelmien tarkasteluun. Tutkimukset johtivat siihen, että organisaatioita alettiin tarkastella sekä sosiaalisina, teknisinä että taloudellisina järjestelminä

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#anki #johtamisajattelu #kehittyminen #markkinointiajattelu

organisaatio pyrkii sopeutumaan ympäristön aiheuttamaan epävarmuuteen tiedonvaihdon ja tietojen prosessoinnin avulla

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#1.5 #am #am-lk1 #johtamis-ja_markkinointiajattelun_kehittyminen #tuotantokeskeisestä_ajattelusta_asiakaslähtöiseenmarkkinointiin

Markkinointiajattelu selittää yritysten ja asiakkaiden käyttäytymistä erilaisissa markkinoinnin tilanteissa.

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#1.5 #am #am-lk1 #johtamis-ja_markkinointiajattelun_kehittyminen #tuotantokeskeisestä_ajattelusta_asiakaslähtöiseenmarkkinointiin

Markkinoinnin tieteenä katsotaan syntyneen 1960-luvulla ja saaneen alkunsa Harvard Business Review’n artikkelista ”Marketing Myopia”, jossa professori Ted Levitt kuvaa kilpailun ja asiakkaiden ratkaisevaa roolia liiketoiminnassa

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#sleep

The Cardinal men’s basketball team volunteered to be Mah’s study cohort. Eleven players used motion-sensing wristbands to determine how long they slept on average—just over 6.5 hours a night. For two weeks, the team kept to their normal schedules, while Mah’s researchers measured their performances on sprint drills, free throws, and three-point shooting. Then, the players were told to try and sleep as much as they could for five to seven weeks, with a goal of 10 hours in bed each night. Their actual time asleep, as measured by the sensors attached to their wrists, went from an average of 6.5 hours to nearly 8.5 hours.

The results were startling. By the end of the extra-sleep period, players had improved their free throw shooting by 11.4 percent and their three-point shooting by 13.7 percent. There was an improvement of 0.7 seconds on the 282-foot sprint drill—every single player on the team was quicker than before the study had started.

A 13-percent performance enhancement is the sort of gain that one associates with drugs or years of training—not simply making sure to get tons of sleep.

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weeks trying to extend their sleep as much as possible, to see what effect it would have on objective measurements of athletic performance. Amazingly, no one had ever done a study to see the effect of sleep extension on competitive athletes. <span>The Cardinal men’s basketball team volunteered to be Mah’s study cohort. Eleven players used motion-sensing wristbands to determine how long they slept on average—just over 6.5 hours a night. For two weeks, the team kept to their normal schedules, while Mah’s researchers measured their performances on sprint drills, free throws, and three-point shooting. Then, the players were told to try and sleep as much as they could for five to seven weeks, with a goal of 10 hours in bed each night. Their actual time asleep, as measured by the sensors attached to their wrists, went from an average of 6.5 hours to nearly 8.5 hours. The results were startling. By the end of the extra-sleep period, players had improved their free throw shooting by 11.4 percent and their three-point shooting by 13.7 percent. There was an improvement of 0.7 seconds on the 282-foot sprint drill—every single player on the team was quicker than before the study had started. A 13-percent performance enhancement is the sort of gain that one associates with drugs or years of training—not simply making sure to get tons of sleep. Mah’s research strongly suggests that most athletes would perform much better with more sleep—if they could get it. But it’s not quite that easy; in fact, athletes face challenges with

Tags

#asdf #definition #linear-algebra

Question

Def: **composition of functions**

Answer

Given two functions f : A → B and g : B → C, the function g ◦ f, called the composition of g and f, is a function whose domain is A and its co-domain is C. It is defined by the rule

(g ◦ f)(x )=g(f(x))

[$$]\forall x \in A[/$$].

If the image of f is not contain ed in the dom ain of g then g ◦ f is not a legal expression.

(g ◦ f)(x )=g(f(x))

[$$]\forall x \in A[/$$].

If the image of f is not contain ed in the dom ain of g then g ◦ f is not a legal expression.

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Tags

#asdf #definition #linear-algebra #theorem

Question

Theorem: *Associativity of composition*

Answer

For functions f, g, h,

h ◦ (g ◦ f) = (h ◦ g) ◦ f

if the compositions are legal.

h ◦ (g ◦ f) = (h ◦ g) ◦ f

if the compositions are legal.

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

#asdf #definition #linear-algebra

Question

Def: *functional inverse*

Answer

We say that functions *f* and *g* are functional inverses of each other if

•*f ◦ g* is defined and is the identity function on the domain of *g*, and

•*g ◦ f* is defined and is the identity function on the domain of *f*.

•

•

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

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Tags

#cloze #linear-algebra

Question

A function that has an inverse is said to be *{{c1::invertible}}.*

Answer

Not every function has an inverse.

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scheduled repetition interval | last repetition or drill |

Tags

#asdf #definition #linear-algebra

Question

Def: **one-to-one**

Answer

Consider a function *f : D → F* .

We say that*f* is one-to-one if for every *x, y* ∈ *D*, *f*(*x*) = *f*(*y*) *⇒ x* = *y*.

We say that

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scheduled repetition interval | last repetition or drill |

Tags

#cloze #definition #linear-algebra

Question

[$$] f: D \mapsto F[/$$]

We say that*f* is *{{c1::onto}} *if, for every *z* ∈ *F* ,there exists *x* ∈ *D* such that *f*(*x*) = *z*.

We say that

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

#cloze #linear-algebra #theorem

Question

Lemma: An invertible function is {{c1::one-to-one}}.

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |