Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeta-learning for mixed linear regression
433
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In modern supervised learning, there are a large number of tasks, but many of them are associated with only a small amount of labeled data. These include data from medical image processing and robotic interaction. Even though each individual task cannot be meaningfully trained in isolation, one seeks to meta-learn across the tasks from past experiences by exploiting some similarities. We study a fundamental question of interest: When can abundant tasks with small data compensate for lack of tasks with big data? We focus on a canonical scenario where each task is drawn from a mixture of $k$ linear regressions, and identify sufficient conditions for such a graceful exchange to hold; The total number of examples necessary with only small data tasks scales similarly as when big data tasks are available. To this end, we introduce a novel spectral approach and show that we can efficiently utilize small data tasks with the help of $tildeOmega(k^{3/2})$ medium data tasks each with $tildeOmega(k^{1/2})$ examples.
rate research
Read More
A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of k linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with $Omega(k^{1/2})$ examples each. However, this algorithm is brittle in two important scenarios. The predictions can be arbitrarily bad (i) even with only a few outliers in the dataset; or (ii) even if the medium-sized tasks are slightly smaller with $o(k^{1/2})$ examples each. We introduce a spectral approach that is simultaneously robust under both scenarios. To this end, we first design a novel outlier-robust principal component analysis algorithm that achieves an optimal accuracy. This is followed by a sum-of-squares algorithm to exploit the information from higher order moments. Together, this approach is robust against outliers and achieves a graceful statistical trade-off; the lack of $Omega(k^{1/2})$-size tasks can be compensated for with smaller tasks, which can now be as small as $O(log k)$.
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are very fast and simple. In this paper we analyze ILTS in the setting of mixed linear regression with corruptions (MLR-C). We first establish deterministic conditions (on the features etc.) under which the ILTS iterate converges linearly to the closest mixture component. We also provide a global algorithm that uses ILTS as a subroutine, to fully solve mixed linear regressions with corruptions. We then evaluate it for the widely studied setting of isotropic Gaussian features, and establish that we match or better existing results in terms of sample complexity. Finally, we provide an ODE analysis for a gradient-descent variant of ILTS that has optimal time complexity. Our results provide initial theoretical evidence that iteratively fitting to the best subset of samples -- a potentially widely applicable idea -- can provably provide state of the art performance in bad training data settings.
Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still perform poorly in practice, particularly in presence of real world non-stationary signals and drift. This paper describes a flexible method that can generate symmetric and asymmetric uncertainty estimates, makes no assumptions about stationarity, and outperforms competitive baselines on both drift and non drift scenarios. This work helps make sequential regression more effective and practical for use in real-world applications, and is a powerful new addition to the modeling toolbox for sequential uncertainty quantification in general.
Meta-learning algorithms aim to learn two components: a model that predicts targets for a task, and a base learner that quickly updates that model when given examples from a new task. This additional level of learning can be powerful, but it also creates another potential source for overfitting, since we can now overfit in either the model or the base learner. We describe both of these forms of metalearning overfitting, and demonstrate that they appear experimentally in common meta-learning benchmarks. We then use an information-theoretic framework to discuss meta-augmentation, a way to add randomness that discourages the base learner and model from learning trivial solutions that do not generalize to new tasks. We demonstrate that meta-augmentation produces large complementary benefits to recently proposed meta-regularization techniques.
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data that are not independently sampled. In particular, the error bound applies to certain time series generated by well-known classes of dynamical models, such as ARX models.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
