Database Reference
In-Depth Information
3.1 An Overview About How to Learn from Data
Statistical learning is about learning from seen data in order to predict unseen
data with minimal error. Data comprise inputs
x
represented by a vector with
a fixed number of dimensions
∈X ↂ
R
p
) from the input space
.In
our problem,
x
is a video, represented by a vector of measurements from video
sessions' activity.
In supervised learning, each input measurement is coupled with a
p
(
x
X
y
, a label
selected by an oracle, from the output space
)
drawn
independently and identically distributed
(i.i.d.) from a fixed but unknown
joint probability density
Y
. To learn, we take
N
pairs (
x
,y
). This is true for both training and testing
datasets. For instance, we consider the training dataset
Pr
(
X, Y
x
i
,y
i
}
i
=1
of
S
=
{
N
pairs (
x
,y
). Using this dataset, the supervised learning algorithm searches for a
function
. State-of-the-art algorithms, such
as
support vector machines
(SVM)[
11
]or
ensemble methods
[
16
], aim to find
f
in
f
:
Xₒ
R
in a fixed function class
F
F
with the lowest empirical risk defined as:
f
∈
arg min
f ∈F
r
emp
(
f
)
(1)
i
=1
I
{f
(
x
)
=
y
i
}
is computed over the training set, and
)=
1
N
where
r
emp
(
f
I
{.}
is
the indicator function which returns 1 if the predicate
{.}
is true and 0 otherwise.
In other terms,
r
emp
is a quality measure relating the label to the prediction
provided by the function
.
To model our prediction problem, we use a statistical learning approach
called learning-to-rank. This approach has been a hot topic in Machine Learn-
ing community for the last 10 years. It combines properties of two well-known
other approaches: regression, where
f
on the training dataset
S
y ∈Yↂ
R
; classification where
y ∈Yↂ
{
0
,
1
, ..., K}
with
K ≥
1. In learning-to-rank approach,
y
gives an indication on
the target order (formally represented by a permutation
σ ∈
ʣ).
3.2 A Ranking Model for Internet Videos
The main purpose of our learning model is to capture popularity growth dynam-
ics and system resources availability of peer-assisted VoD systems. Therefore, we
assume that prediction model must allow us to rank Internet videos in order of
demand. This can be modelled as a learning-to-rank problem.
Given an i.i.d. sample (
x
,y
) such as described in Subsect.
3.1
, we model
inputs and outputs as follows.
Inputs.
We represent the input space
x
is a video described as 10 lightweight
measurements from the request arrival process. These measurements are video
size, network availability, network usage (load), current number of viewers and
replicas, inter-arrival time between requests (delta), aggregate number of views,
mean of time between requests (mtbr), life time, and average bitrate. We com-
pute averages and means from up to the five last requests. Our goal is to gather
as much information about users' interactions as possible in an easy manner to
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