Learning Aggregation Functions

• URL: http://arxiv.org/abs/2012.08482v1
• Date: Tue, 15 Dec 2020 18:28:53 GMT
• Title: Learning Aggregation Functions
• Authors: Giovanni Pellegrini and Alessandro Tibo and Paolo Frasconi and Andrea Passerini and Manfred Jaeger
• Abstract summary: We introduce LAF (Learning Aggregation Functions), a learnable aggregator for sets of arbitrary cardinality. We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures.
• Score: 78.47770735205134
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce LAF (Learning Aggregation Functions), a learnable aggregator for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g. variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation.

Related papers

• Fast and interpretable Support Vector Classification based on the truncated ANOVA decomposition [0.0]
  Support Vector Machines (SVMs) are an important tool for performing classification on scattered data. We propose solving SVMs in primal form using feature maps based on trigonometric functions or wavelets.
  arXiv  Detail & Related papers  (2024-02-04T10:27:42Z)
• Complexity-Theoretic Implications of Multicalibration [8.315801422499863]
  Multiaccurate predictors satisfy a stronger condition: they are calibrated on each set in the collection. This complexity-theoretic Regularity Lemma is known to have implications in different areas. We show that every function (regardless of its hardness) has a small collection of disjoint hardcore sets.
  arXiv  Detail & Related papers  (2023-12-28T18:53:21Z)
• Agnostically Learning Multi-index Models with Queries [54.290489524576756]
  We study the power of query access for the task of agnostic learning under the Gaussian distribution. We show that query access gives significant runtime improvements over random examples for agnostically learning MIMs.
  arXiv  Detail & Related papers  (2023-12-27T15:50:47Z)
• SPINE: Soft Piecewise Interpretable Neural Equations [0.0]
  Fully connected networks are ubiquitous but uninterpretable. This paper takes a novel approach to piecewise fits by using set operations on individual pieces(parts) It can find a variety of applications where fully connected layers must be replaced by interpretable layers.
  arXiv  Detail & Related papers  (2021-11-20T16:18:00Z)
• ORSA: Outlier Robust Stacked Aggregation for Best- and Worst-Case Approximations of Ensemble Systems\ [0.0]
  In Post-Silicon Validation for semiconductor devices (PSV), the task is to approximate the underlying function of the data with multiple learning algorithms. In PSV, the expectation is that an unknown number of subsets describe functions showing very different characteristics. Our method aims to find a suitable approximation that is robust to outliers and represents the best or worst case in a way that will apply to as many types as possible.
  arXiv  Detail & Related papers  (2021-11-17T11:33:46Z)
• Fuzzy Clustering with Similarity Queries [56.96625809888241]
  The fuzzy or soft objective is a popular generalization of the well-known $k$-means problem. We show that by making few queries, the problem becomes easier to solve.
  arXiv  Detail & Related papers  (2021-06-04T02:32:26Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces [208.67848059021915]
  We study the exploration-exploitation tradeoff at the core of reinforcement learning. In particular, we prove that the complexity of the function class $mathcalF$ characterizes the complexity of the function. Our regret bounds are independent of the number of episodes.
  arXiv  Detail & Related papers  (2020-11-09T18:32:22Z)
• From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models [82.95892656532696]
  Submodular functions have been studied extensively in machine learning and data mining. In this work, we propose a continuous DR-submodular extension for integer submodular functions. We formulate a new probabilistic model which is defined through integer submodular functions.
  arXiv  Detail & Related papers  (2020-06-01T22:20:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.