Expected Information Maximization: Using the I-Projection for Mixture Density Estimation

• URL: http://arxiv.org/abs/2001.08682v1
• Date: Thu, 23 Jan 2020 17:24:50 GMT
• Title: Expected Information Maximization: Using the I-Projection for Mixture Density Estimation
• Authors: Philipp Becker, Oleg Arenz, Gerhard Neumann
• Abstract summary: Modelling highly multi-modal data is a challenging problem in machine learning. We present a new algorithm called Expected Information Maximization (EIM) for computing the I-projection. We show that our algorithm is much more effective in computing the I-projection than recent GAN approaches.
• Score: 22.096148237257644
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The M-projection forces the model to average over modes it cannot represent. In contrast, the I(information)-projection ignores such modes in the data and concentrates on the modes the model can represent. Such behavior is appealing whenever we deal with highly multi-modal data where modelling single modes correctly is more important than covering all the modes. Despite this advantage, the I-projection is rarely used in practice due to the lack of algorithms that can efficiently optimize it based on data. In this work, we present a new algorithm called Expected Information Maximization (EIM) for computing the I-projection solely based on samples for general latent variable models, where we focus on Gaussian mixtures models and Gaussian mixtures of experts. Our approach applies a variational upper bound to the I-projection objective which decomposes the original objective into single objectives for each mixture component as well as for the coefficients, allowing an efficient optimization. Similar to GANs, our approach employs discriminators but uses a more stable optimization procedure, using a tight upper bound. We show that our algorithm is much more effective in computing the I-projection than recent GAN approaches and we illustrate the effectiveness of our approach for modelling multi-modal behavior on two pedestrian and traffic prediction datasets.

Related papers

• Decoding-Time Language Model Alignment with Multiple Objectives [88.64776769490732]
  Existing methods primarily focus on optimizing LMs for a single reward function, limiting their adaptability to varied objectives. Here, we propose $textbfmulti-objective decoding (MOD)$, a decoding-time algorithm that outputs the next token from a linear combination of predictions. We show why existing approaches can be sub-optimal even in natural settings and obtain optimality guarantees for our method.
  arXiv  Detail & Related papers  (2024-06-27T02:46:30Z)
• Towards Efficient Pareto Set Approximation via Mixture of Experts Based Model Fusion [53.33473557562837]
  Solving multi-objective optimization problems for large deep neural networks is a challenging task due to the complexity of the loss landscape and the expensive computational cost. We propose a practical and scalable approach to solve this problem via mixture of experts (MoE) based model fusion. By ensembling the weights of specialized single-task models, the MoE module can effectively capture the trade-offs between multiple objectives.
  arXiv  Detail & Related papers  (2024-06-14T07:16:18Z)
• MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation [80.47072100963017]
  Model merging is an effective approach to combine multiple single-task models, fine-tuned from the same pre-trained model, into a multitask model. Existing model-merging methods focus on enhancing average task accuracy. We introduce a novel low-compute algorithm, Model Merging with Amortized Pareto Front (MAP)
  arXiv  Detail & Related papers  (2024-06-11T17:55:25Z)
• Stable Training of Probabilistic Models Using the Leave-One-Out Maximum Log-Likelihood Objective [0.7373617024876725]
  Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. An adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. A modified expectation-maximization algorithm is employed to accelerate the optimization speed reliably.
  arXiv  Detail & Related papers  (2023-10-05T14:08:42Z)
• Efficient Training of Energy-Based Models Using Jarzynski Equality [13.636994997309307]
  Energy-based models (EBMs) are generative models inspired by statistical physics. The computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality can be used to perform this computation efficiently.
  arXiv  Detail & Related papers  (2023-05-30T21:07:52Z)
• A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data [0.0]
  We introduce an innovative algorithm that evaluates cluster effects for new data points, thereby increasing the robustness and precision of this model. The inferential and predictive efficacy of this approach is further illustrated through its application in student scoring and protein expression.
  arXiv  Detail & Related papers  (2023-02-06T23:34:51Z)
• HyperImpute: Generalized Iterative Imputation with Automatic Model Selection [77.86861638371926]
  We propose a generalized iterative imputation framework for adaptively and automatically configuring column-wise models. We provide a concrete implementation with out-of-the-box learners, simulators, and interfaces.
  arXiv  Detail & Related papers  (2022-06-15T19:10:35Z)
• Learning Distributionally Robust Models at Scale via Composite Optimization [45.47760229170775]
  We show how different variants of DRO are simply instances of a finite-sum composite optimization for which we provide scalable methods. We also provide empirical results that demonstrate the effectiveness of our proposed algorithm with respect to the prior art in order to learn robust models from very large datasets.
  arXiv  Detail & Related papers  (2022-03-17T20:47:42Z)
• Model-Agnostic Multitask Fine-tuning for Few-shot Vision-Language Transfer Learning [59.38343286807997]
  We propose Model-Agnostic Multitask Fine-tuning (MAMF) for vision-language models on unseen tasks. Compared with model-agnostic meta-learning (MAML), MAMF discards the bi-level optimization and uses only first-order gradients. We show that MAMF consistently outperforms the classical fine-tuning method for few-shot transfer learning on five benchmark datasets.
  arXiv  Detail & Related papers  (2022-03-09T17:26:53Z)
• Conservative Objective Models for Effective Offline Model-Based Optimization [78.19085445065845]
  Computational design problems arise in a number of settings, from synthetic biology to computer architectures. We propose a method that learns a model of the objective function that lower bounds the actual value of the ground-truth objective on out-of-distribution inputs. COMs are simple to implement and outperform a number of existing methods on a wide range of MBO problems.
  arXiv  Detail & Related papers  (2021-07-14T17:55:28Z)
• Variational Model-based Policy Optimization [34.80171122943031]
  Model-based reinforcement learning (RL) algorithms allow us to combine model-generated data with those collected from interaction with the real system in order to alleviate the data efficiency problem in RL. We propose an objective function as a variational lower-bound of a log-likelihood of a log-likelihood to jointly learn and improve model and policy. Our experiments on a number of continuous control tasks show that despite being more complex, our model-based (E-step) algorithm, called emactoral model-based policy optimization (VMBPO), is more sample-efficient and
  arXiv  Detail & Related papers  (2020-06-09T18:30:15Z)

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.