Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeta Learning in the Continuous Time Limit
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we establish the ordinary differential equation (ODE) that underlies the training dynamics of Model-Agnostic Meta-Learning (MAML). Our continuous-time limit view of the process eliminates the influence of the manually chosen step size of gradient descent and includes the existing gradient descent training algorithm as a special case that results from a specific discretization. We show that the MAML ODE enjoys a linear convergence rate to an approximate stationary point of the MAML loss function for strongly convex task losses, even when the corresponding MAML loss is non-convex. Moreover, through the analysis of the MAML ODE, we propose a new BI-MAML training algorithm that significantly reduces the computational burden associated with existing MAML training methods. To complement our theoretical findings, we perform empirical experiments to showcase the superiority of our proposed methods with respect to the existing work.
rate research
Read More
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laboriously simulating the intractable dynamics of the assumed CTBN. This is a problem, especially for structure learning tasks, where this has to be done for each element of a super-exponentially growing set of possible structures. In order to circumvent this notorious bottleneck, we develop a novel gradient-based approach to structure learning. Instead of sampling and scoring all possible structures individually, we assume the generator of the CTBN to be composed as a mixture of generators stemming from different structures. In this framework, structure learning can be performed via a gradient-based optimization of mixture weights. We combine this approach with a new variational method that allows for a closed-form calculation of this mixture marginal likelihood. We show the scalability of our method by learning structures of previously inaccessible sizes from synthetic and real-world data.
While neural networks are powerful function approximators, they suffer from catastrophic forgetting when the data distribution is not stationary. One particular formalism that studies learning under non-stationary distribution is provided by continual learning, where the non-stationarity is imposed by a sequence of distinct tasks. Most methods in this space assume, however, the knowledge of task boundaries, and focus on alleviating catastrophic forgetting. In this work, we depart from this view and move the focus towards faster remembering -- i.e measuring how quickly the network recovers performance rather than measuring the networks performance without any adaptation. We argue that in many settings this can be more effective and that it opens the door to combining meta-learning and continual learning techniques, leveraging their complementary advantages. We propose a framework specific for the scenario where no information about task boundaries or task identity is given. It relies on a separation of concerns into what task is being solved and how the task should be solved. This framework is implemented by differentiating task specific parameters from task agnostic parameters, where the latter are optimized in a continual meta learning fashion, without access to multiple tasks at the same time. We showcase this framework in a supervised learning scenario and discuss the implication of the proposed formalism.
The inaccessibility of controlled randomized trials due to inherent constraints in many fields of science has been a fundamental issue in causal inference. In this paper, we focus on distinguishing the cause from effect in the bivariate setting under limited observational data. Based on recent developments in meta learning as well as in causal inference, we introduce a novel generative model that allows distinguishing cause and effect in the small data setting. Using a learnt task variable that contains distributional information of each dataset, we propose an end-to-end algorithm that makes use of similar training datasets at test time. We demonstrate our method on various synthetic as well as real-world data and show that it is able to maintain high accuracy in detecting directions across varying dataset sizes.
This paper introduces a new framework for data efficient and versatile learning. Specifically: 1) We develop ML-PIP, a general framework for Meta-Learning approximate Probabilistic Inference for Prediction. ML-PIP extends existing probabilistic interpretations of meta-learning to cover a broad class of methods. 2) We introduce VERSA, an instance of the framework employing a flexible and versatile amortization network that takes few-shot learning datasets as inputs, with arbitrary numbers of shots, and outputs a distribution over task-specific parameters in a single forward pass. VERSA substitutes optimization at test time with forward passes through inference networks, amortizing the cost of inference and relieving the need for second derivatives during training. 3) We evaluate VERSA on benchmark datasets where the method sets new state-of-the-art results, handles arbitrary numbers of shots, and for classification, arbitrary numbers of classes at train and test time. The power of the approach is then demonstrated through a challenging few-shot ShapeNet view reconstruction task.
Hyperparameter optimization in machine learning (ML) deals with the problem of empirically learning an optimal algorithm configuration from data, usually formulated as a black-box optimization problem. In this work, we propose a zero-shot method to meta-learn symbolic default hyperparameter configurations that are expressed in terms of the properties of the dataset. This enables a much faster, but still data-dependent, configuration of the ML algorithm, compared to standard hyperparameter optimization approaches. In the past, symbolic and static default values have usually been obtained as hand-crafted heuristics. We propose an approach of learning such symbolic configurations as formulas of dataset properties from a large set of prior evaluations on multiple datasets by optimizing over a grammar of expressions using an evolutionary algorithm. We evaluate our method on surrogate empirical performance models as well as on real data across 6 ML algorithms on more than 100 datasets and demonstrate that our method indeed finds viable symbolic defaults.
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
