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DL(14) Learning in Sequential Domain - Coggle Diagram
DL(14) Learning in Sequential Domain
Sequence
an external vertex, or an ordered pair (t,h) where the head
h
is a vertex and the tail
t
is a sequence.
A
Transdtuction T : X* → O
algebraic
if it has
0 finite memory
casual
if the output at time t does not depend on
future
inputs at time t+1, t+2, ...
finite memory k
if ∀ x ∈ X* and ∀t, T(x(t)) only depends on {x(t), x(t-1), ..., x(t-k)}
stationary
if f(∙), g(∙) do not depent on t
why learning in
sequential domain
is different wrt
static domain
?
because successive points in sequential data are strongly correlated
machine learning models for
sequence learning
have to
deal with sequential variations
make use of contextual information
consider that data points are not independent
Learn
P(o|x)
Static Data
typeof(x)
: fixed-size tuple of predictive attributes
typeof(o)
Classification
: a categorical variable
Regression
: a numerical (multivariate variable)
Sequential Data
typeof(x)
: a
sequence x(1),...,x(t)
,... where each x(t) has a static type
typeof(o)
: may be either static or a sequence
Recursive State Representation
o
(t) = g (
h
(t),
x
(t), t)
g
: H x X → O
output function
h
(t) = f (
h
(t-1),
x
(t), t)
f
: H x X → H
state transition function
q^-1
h(t)
=
h(t-1)