1,238 research outputs found
Jeffreys's law for general games of prediction: in search of a theory
We are interested in the following version of Jeffreys's law: if two
predictors are predicting the same sequence of events and either is doing a
satisfactory job, they will make similar predictions in the long run. We give a
classification of instances of Jeffreys's law, illustrated with examples.Comment: 12 page
Prediction with Expert Advice under Discounted Loss
We study prediction with expert advice in the setting where the losses are
accumulated with some discounting---the impact of old losses may gradually
vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm
for Regression to this case, propose a suitable new variant of exponential
weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte
Leading strategies in competitive on-line prediction
We start from a simple asymptotic result for the problem of on-line
regression with the quadratic loss function: the class of continuous
limited-memory prediction strategies admits a "leading prediction strategy",
which not only asymptotically performs at least as well as any continuous
limited-memory strategy but also satisfies the property that the excess loss of
any continuous limited-memory strategy is determined by how closely it imitates
the leading strategy. More specifically, for any class of prediction strategies
constituting a reproducing kernel Hilbert space we construct a leading
strategy, in the sense that the loss of any prediction strategy whose norm is
not too large is determined by how closely it imitates the leading strategy.
This result is extended to the loss functions given by Bregman divergences and
by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006
proceeding
The Fundamental Nature of the Log Loss Function
The standard loss functions used in the literature on probabilistic
prediction are the log loss function, the Brier loss function, and the
spherical loss function; however, any computable proper loss function can be
used for comparison of prediction algorithms. This note shows that the log loss
function is most selective in that any prediction algorithm that is optimal for
a given data sequence (in the sense of the algorithmic theory of randomness)
under the log loss function will be optimal under any computable proper mixable
loss function; on the other hand, there is a data sequence and a prediction
algorithm that is optimal for that sequence under either of the two other
standard loss functions but not under the log loss function.Comment: 12 page
Competing with stationary prediction strategies
In this paper we introduce the class of stationary prediction strategies and
construct a prediction algorithm that asymptotically performs as well as the
best continuous stationary strategy. We make mild compactness assumptions but
no stochastic assumptions about the environment. In particular, no assumption
of stationarity is made about the environment, and the stationarity of the
considered strategies only means that they do not depend explicitly on time; we
argue that it is natural to consider only stationary strategies even for highly
non-stationary environments.Comment: 20 page
New Achievements in the Field of Impulse Processing Technologies
The outcomes of research in the field of application of high pressure in a process engineering are stated. The high pressure is created by impulsive sources of energy, such as explosion of condensed explosive substances and gaseous detonatable mixtures. Application of high pressure created by explosion for technological processes of sheet forming parts from metal and non-metal materials is considered. In the latter case, the mechanical properties in the process polymerisation of composite materials in the outcome of the impulsive loading significantly rise. The impulsive high pressure has a significant impact on handling - compressing of powder materials, on manufacture of special products, foundry forms and ont destruction of rods in molten products
Criteria of efficiency for conformal prediction
We study optimal conformity measures for various criteria of efficiency of
classification in an idealised setting. This leads to an important class of
criteria of efficiency that we call probabilistic; it turns out that the most
standard criteria of efficiency used in literature on conformal prediction are
not probabilistic unless the problem of classification is binary. We consider
both unconditional and label-conditional conformal prediction.Comment: 31 page
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