status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
[...] are used by firms to sell debt or equity to raise long-term capital to finance the production of goods and services.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
[...] can be defined as the branch of microeconomics that relates [...] to consumer preferences.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
We can represent the utility function as
U=f(Qx1,Qx2,...,Qxn)
where the Qs are the quantities of [...].
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Implicit costs are not [...]in a financial system.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Analysts also need to compare (3things) [...] before and after the replacement to identify changes in these elements.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Economic income is an investment's [...] plus the [...].
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Free cash flow (FCF) is a measure of a company's [...]
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The term [...]means that the revenue number is reported after adjustments.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
[...] is an accrual accounting technique used to allocate the cost of extracting natural resources such as timber, minerals and oil from the earth.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The five major items found in the current assets section are:
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The IRR and NPV rules rank projects differently when
the [...] cash flows differs.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Since the objective function is unknown, the Bayesian strategy (of optimisation) is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be.
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form
where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L.
Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition.^{[2]} If the matrix A is Hermitian and positive semi-definite, then it still has a decomposition of the form A = LL* if the diagonal entries of L are allowed to be zero.^{[3]}
When A has real entries, L has real entries as well, and the factorization may be written A = LL^{T}.^{[4]}
The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*. However, the decomposition need not be unique when A is positive semidefinite.
The converse holds trivially: if A can be written as LL* for some invertible L, lower triangular or otherwise, then A is Hermitian and positive definite.
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Expecatation propagation aims to minimise \(KL(p(x,\theta\mid y,m)\parallel q(x,\theta\mid m))\). The problem with this minimisation, is that \( p(x,\theta\mid y,m)\) is unknown, so the first thing we do is to force some structure on this distribution, by making assumptions. For many models with IID observation, the posterior can be factorised as
$$ p(\theta \mid D) = \frac{1}{p(D)} p(\theta) \prod_{i=1}^{N} p(x^{(i)} \mid \theta) $$
which is a product of prior and likelihood, normalised by the data likelihood. Ignoring the constant, we can rearrange the posterior as
$$ p(\theta \mid D) \propto \prod_{i=0}^{N} f_i(\theta) $$
with \(f_0(\theta) = p(\theta) \) and \( f_i(\theta) = p(x^{(i)} \mid \theta) .\) And now our goal is to find a factorable
$$q(\theta) = \prod_{i=0}^{N} \tilde{f_i}(\theta) $$
that is close to our posterior.
EP manages this with a Gibbs sampling like procedure by
$$ \min_{\tilde{f_i}(\theta)} KL \left( f_i(\theta) \prod_{j \neq i}^{N} \tilde{f_j}(\theta) \parallel \tilde{f_i}(\theta) \prod_{j \neq i}^{N} \tilde{f_j}(\theta) \right) $$
and updating one factor at a time. The complete proceduce is as follows:
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The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form
where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L.
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The Cholesky decomposition is of the form [...]
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In Cholesky decomposition of the form L is a [...]
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Hermitian matrices can be understood as the complex extension of
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Hermitian matrices can be understood as the [...] of real symmetric matrices.
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OOP is about producing [...] — an important determinant of productivity
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Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x
e i x = cos x + i sin x , {\displaystyle e^{ix}=\cos x+i\sin x,}where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians.
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Variational Bayesian methods are primarily used for two purposes:
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[edit]
Michalis Titsias ; Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:567-574, 2009.status | not read | reprioritisations | ||
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