E-resources
-
Oneto, Luca; Ridella, Sandro
Entropy (Basel, Switzerland), 01/2021, Volume: 23, Issue: 1Journal Article
In this paper, we deal with the classical Statistical Learning Theory's problem of bounding, with high probability, the true risk R(h) of a hypothesis chosen from a set H of hypotheses. The Union Bound (UB) allows one to state that PLR^(h),δqh≤R(h)≤UR^(h),δph≥1-δ where R^(h) is the empirical errors, if it is possible to prove that P{R(h)≥L(R^(h),δ)}≥1-δ and P{R(h)≤U(R^(h),δ)}≥1-δ, when , qh, and ph are chosen before seeing the data such that qh,ph∈0,1 and ∑h∈H(qh+ph)=1. If no information is available qh and ph are set to 12m, namely equally distributed. This approach gives poor results since, as a matter of fact, a learning procedure targets just particular hypotheses, namely hypotheses with small empirical error, disregarding the others. In this work we set the qh and ph in a distribution-dependent way increasing the probability of being chosen to function with small true risk. We will call this proposal Distribution-Dependent Weighted UB (DDWUB) and we will retrieve the sufficient conditions on the choice of qh and ph that state that DDWUB outperforms or, in the worst case, degenerates into UB. Furthermore, theoretical and numerical results will show the applicability, the validity, and the potentiality of DDWUB.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.