36,061 research outputs found
Fast learning rates in statistical inference through aggregation
We develop minimax optimal risk bounds for the general learning task
consisting in predicting as well as the best function in a reference set
up to the smallest possible additive term, called the convergence
rate. When the reference set is finite and when denotes the size of the
training data, we provide minimax convergence rates of the form
with tight evaluation of the positive
constant and with exact , the latter value depending on the
convexity of the loss function and on the level of noise in the output
distribution. The risk upper bounds are based on a sequential randomized
algorithm, which at each step concentrates on functions having both low risk
and low variance with respect to the previous step prediction function. Our
analysis puts forward the links between the probabilistic and worst-case
viewpoints, and allows to obtain risk bounds unachievable with the standard
statistical learning approach. One of the key ideas of this work is to use
probabilistic inequalities with respect to appropriate (Gibbs) distributions on
the prediction function space instead of using them with respect to the
distribution generating the data. The risk lower bounds are based on
refinements of the Assouad lemma taking particularly into account the
properties of the loss function. Our key example to illustrate the upper and
lower bounds is to consider the -regression setting for which an
exhaustive analysis of the convergence rates is given while ranges in
.Comment: Published in at http://dx.doi.org/10.1214/08-AOS623 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Randomized Reference Classifier with Gaussian Distribution and Soft Confusion Matrix Applied to the Improving Weak Classifiers
In this paper, an issue of building the RRC model using probability
distributions other than beta distribution is addressed. More precisely, in
this paper, we propose to build the RRR model using the truncated normal
distribution. Heuristic procedures for expected value and the variance of the
truncated-normal distribution are also proposed. The proposed approach is
tested using SCM-based model for testing the consequences of applying the
truncated normal distribution in the RRC model. The experimental evaluation is
performed using four different base classifiers and seven quality measures. The
results showed that the proposed approach is comparable to the RRC model built
using beta distribution. What is more, for some base classifiers, the
truncated-normal-based SCM algorithm turned out to be better at discovering
objects coming from minority classes.Comment: arXiv admin note: text overlap with arXiv:1901.0882
Multi-party Poisoning through Generalized -Tampering
In a poisoning attack against a learning algorithm, an adversary tampers with
a fraction of the training data with the goal of increasing the
classification error of the constructed hypothesis/model over the final test
distribution. In the distributed setting, might be gathered gradually from
data providers who generate and submit their shares of
in an online way.
In this work, we initiate a formal study of -poisoning attacks in
which an adversary controls of the parties, and even for each
corrupted party , the adversary submits some poisoned data on
behalf of that is still "-close" to the correct data (e.g.,
fraction of is still honestly generated). For , this model
becomes the traditional notion of poisoning, and for it coincides with
the standard notion of corruption in multi-party computation.
We prove that if there is an initial constant error for the generated
hypothesis , there is always a -poisoning attacker who can decrease
the confidence of (to have a small error), or alternatively increase the
error of , by . Our attacks can be implemented in
polynomial time given samples from the correct data, and they use no wrong
labels if the original distributions are not noisy.
At a technical level, we prove a general lemma about biasing bounded
functions through an attack model in which each
block might be controlled by an adversary with marginal probability
in an online way. When the probabilities are independent, this coincides with
the model of -tampering attacks, thus we call our model generalized
-tampering. We prove the power of such attacks by incorporating ideas from
the context of coin-flipping attacks into the -tampering model and
generalize the results in both of these areas
Counterfactual Estimation and Optimization of Click Metrics for Search Engines
Optimizing an interactive system against a predefined online metric is
particularly challenging, when the metric is computed from user feedback such
as clicks and payments. The key challenge is the counterfactual nature: in the
case of Web search, any change to a component of the search engine may result
in a different search result page for the same query, but we normally cannot
infer reliably from search log how users would react to the new result page.
Consequently, it appears impossible to accurately estimate online metrics that
depend on user feedback, unless the new engine is run to serve users and
compared with a baseline in an A/B test. This approach, while valid and
successful, is unfortunately expensive and time-consuming. In this paper, we
propose to address this problem using causal inference techniques, under the
contextual-bandit framework. This approach effectively allows one to run
(potentially infinitely) many A/B tests offline from search log, making it
possible to estimate and optimize online metrics quickly and inexpensively.
Focusing on an important component in a commercial search engine, we show how
these ideas can be instantiated and applied, and obtain very promising results
that suggest the wide applicability of these techniques
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