857,844 research outputs found
Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss?
Survey data on expectations frequently find evidence that forecasts are biased, rejecting the joint hypothesis of rational expectations and symmetric loss. While the literature has attempted to explain this bias through forecasters' strategic behavior, we propose a simpler explanation based on asymmetric loss. We establish that existing rationality tests are not robust to even small deviations from symmetry and hence have little ability to tell whether the forecaster is irrational or the loss function is asymmetric. We propose new and more general methods for testing forecast rationality jointly with flexible families of loss functions that embed quadratic loss as a special case. An empirical application to survey data on forecasts of nominal output growth shows strong evidence against rationality and symmetric loss. There is considerably weaker evidence against rationality once asymmetric loss is permittedrationality testing, forecasting, asymmetric loss
M-estimation in Low-rank Matrix Factorization: a General Framework
Many problems in science and engineering can be reduced to the recovery of an unknown large matrix from a small number of random linear measurements. Matrix factorization arguably is the most popular approach for low-rank matrix recovery. Many methods have been proposed using different loss functions, for example the most widely used L_2 loss, more robust choices such as L_1 and Huber loss, quantile and expectile loss for skewed data. All of them can be unified into the framework of M-estimation. In this paper, we present a general framework of low-rank matrix factorization based on M-estimation in statistics. The framework mainly involves two steps: firstly we apply Nesterov's smoothing technique to obtain an optimal smooth approximation for non-smooth loss function, such as L_1 and quantile loss; secondly we exploit an alternative updating scheme along with Nesterov's momentum method at each step to minimize the smoothed loss function. Strong theoretical convergence guarantee has been developed for the general framework, and extensive numerical experiments have been conducted to illustrate the performance of proposed algorithm
A Unified Framework for Compositional Fitting of Active Appearance Models
Active Appearance Models (AAMs) are one of the most popular and
well-established techniques for modeling deformable objects in computer vision.
In this paper, we study the problem of fitting AAMs using Compositional
Gradient Descent (CGD) algorithms. We present a unified and complete view of
these algorithms and classify them with respect to three main characteristics:
i) cost function; ii) type of composition; and iii) optimization method.
Furthermore, we extend the previous view by: a) proposing a novel Bayesian cost
function that can be interpreted as a general probabilistic formulation of the
well-known project-out loss; b) introducing two new types of composition,
asymmetric and bidirectional, that combine the gradients of both image and
appearance model to derive better conver- gent and more robust CGD algorithms;
and c) providing new valuable insights into existent CGD algorithms by
reinterpreting them as direct applications of the Schur complement and the
Wiberg method. Finally, in order to encourage open research and facilitate
future comparisons with our work, we make the implementa- tion of the
algorithms studied in this paper publicly available as part of the Menpo
Project.Comment: 39 page
Robust Losses for Decision-Focused Learning
Optimization models used to make discrete decisions often contain uncertain
parameters that are context-dependent and are estimated through prediction. To
account for the quality of the decision made based on the prediction,
decision-focused learning (end-to-end predict-then-optimize) aims at training
the predictive model to minimize regret, i.e., the loss incurred by making a
suboptimal decision. Despite the challenge of this loss function being possibly
non-convex and in general non-differentiable, effective gradient-based learning
approaches have been proposed to minimize the expected loss, using the
empirical loss as a surrogate. However, empirical regret can be an ineffective
surrogate because the uncertainty in the optimization model makes the empirical
regret unequal to the expected regret in expectation. To illustrate the impact
of this inequality, we evaluate the effect of aleatoric and epistemic
uncertainty on the accuracy of empirical regret as a surrogate. Next, we
propose three robust loss functions that more closely approximate expected
regret. Experimental results show that training two state-of-the-art
decision-focused learning approaches using robust regret losses improves
test-sample empirical regret in general while keeping computational time
equivalent relative to the number of training epochs.Comment: 13 pages, 3 figure
A Bayesian Approach toward Active Learning for Collaborative Filtering
Collaborative filtering is a useful technique for exploiting the preference
patterns of a group of users to predict the utility of items for the active
user. In general, the performance of collaborative filtering depends on the
number of rated examples given by the active user. The more the number of rated
examples given by the active user, the more accurate the predicted ratings will
be. Active learning provides an effective way to acquire the most informative
rated examples from active users. Previous work on active learning for
collaborative filtering only considers the expected loss function based on the
estimated model, which can be misleading when the estimated model is
inaccurate. This paper takes one step further by taking into account of the
posterior distribution of the estimated model, which results in more robust
active learning algorithm. Empirical studies with datasets of movie ratings
show that when the number of ratings from the active user is restricted to be
small, active learning methods only based on the estimated model don't perform
well while the active learning method using the model distribution achieves
substantially better performance.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in
Artificial Intelligence (UAI2004
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