22,597 research outputs found
Defensive forecasting for optimal prediction with expert advice
The method of defensive forecasting is applied to the problem of prediction
with expert advice for binary outcomes. It turns out that defensive forecasting
is not only competitive with the Aggregating Algorithm but also handles the
case of "second-guessing" experts, whose advice depends on the learner's
prediction; this paper assumes that the dependence on the learner's prediction
is continuous.Comment: 14 page
Continuous and randomized defensive forecasting: unified view
Defensive forecasting is a method of transforming laws of probability (stated
in game-theoretic terms as strategies for Sceptic) into forecasting algorithms.
There are two known varieties of defensive forecasting: "continuous", in which
Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous
manner and which produces deterministic forecasts, and "randomized", in which
the dependence of Sceptic's moves on the forecasts is arbitrary and
Forecaster's moves are allowed to be randomized. This note shows that the
randomized variety can be obtained from the continuous variety by smearing
Sceptic's moves to make them continuous.Comment: 10 pages. The new version: (1) relaxes the assumption that the
outcome space is finite, and now it is only assumed to be compact; (2) shows
that in the case where the outcome space is finite of cardinality C, the
randomized forecasts can be chosen concentrated on a finite set of
cardinality at most
Competitive on-line learning with a convex loss function
We consider the problem of sequential decision making under uncertainty in
which the loss caused by a decision depends on the following binary
observation. In competitive on-line learning, the goal is to design decision
algorithms that are almost as good as the best decision rules in a wide
benchmark class, without making any assumptions about the way the observations
are generated. However, standard algorithms in this area can only deal with
finite-dimensional (often countable) benchmark classes. In this paper we give
similar results for decision rules ranging over an arbitrary reproducing kernel
Hilbert space. For example, it is shown that for a wide class of loss functions
(including the standard square, absolute, and log loss functions) the average
loss of the master algorithm, over the first observations, does not exceed
the average loss of the best decision rule with a bounded norm plus
. Our proof technique is very different from the standard ones and
is based on recent results about defensive forecasting. Given the probabilities
produced by a defensive forecasting algorithm, which are known to be well
calibrated and to have good resolution in the long run, we use the expected
loss minimization principle to find a suitable decision.Comment: 26 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
On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game
In the framework of the game-theoretic probability of Shafer and Vovk (2001)
it is of basic importance to construct an explicit strategy weakly forcing the
strong law of large numbers (SLLN) in the bounded forecasting game. We present
a simple finite-memory strategy based on the past average of Reality's moves,
which weakly forces the strong law of large numbers with the convergence rate
of . Our proof is very simple compared to a corresponding
measure-theoretic result of Azuma (1967) on bounded martingale differences and
this illustrates effectiveness of game-theoretic approach. We also discuss
one-sided protocols and extension of results to linear protocols in general
dimension.Comment: 14 page
The Politics of IMF Forecasts
Using panel data for 157 countries over the period 1999-2005 we empirically investigate the politics involved in IMF economic forecasts. We find a systematic bias in growth and inflation forecasts. Our results indicate that countries voting in line with the US in the UN General Assembly receive lower inflation forecasts. As the US is the Fund’s major shareholder, this result supports the hypothesis that the Fund’s forecasts are not purely based on economic considerations. We further find inflation forecasts are systematically biased downwards for countries with greater IMF loans outstanding relative to GDP, indicating that the IMF engages in “defensive forecasting.” Countries with a fixed exchange rate regime also receive low inflation forecasts. Considering the detrimental effects that inflation can have under such an exchange rate regime, we consider this evidence consistent with the Fund’s desire to preserve economic stability.IMF; Economic Forecasts; Political Influence
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