We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input-output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on five datasets, of which two are synthetically generated, illustrate clear advantages of our mixture-of-experts method for high-dimensional inputs, outperforming competitor models both in terms of validation metrics and visual inspection.
Université de Caen-Normandie（卡昂-诺曼底大学）；Normandie Université（诺曼底大学）；CNRS（法国国家科学研究中心）
Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal distribution. However, it is known that for data with asymmetric behavior, heavy tails and atypical observations, the use of the normal distribution is unsuitable. We introduce a new robust non-normal mixture of experts modeling using the skew $t$ distribution. The proposed skew $t$ mixture of experts, named STMoE, handles these issues of the normal mixtures expe…
In this paper, we propose a novel mixture of expert architecture for learning polyhedral classifiers. We learn the parameters of the classifierusing an expectation maximization algorithm. Wederive the generalization bounds of the proposedapproach. Through an extensive simulation study, we show that the proposed method performs comparably to other state-of-the-art approaches.
Booth School of Business University of Chicago（芝加哥大学商学院）；Volgenau School of Engineering, George Mason University（乔治·马歇尔大学工程学院）；Department of Systems Engineering and Operations Research George Mason University（乔治·马歇尔大学系统工程与运营管理系）
Mixtures of experts models provide a framework in which covariates may be included in mixture models. This is achieved by modelling the parameters of the mixture model as functions of the concomitant covariates. Given their mixture model foundation, mixtures of experts models possess a diverse range of analytic uses, from clustering observations to capturing parameter heterogeneity in cross-sectional data. This chapter focuses on delineating the mixture of experts modelling framework and demonstrates the utility and flexibility of mixtures of experts models as an analytic tool.
University of Warwick（华威大学）；University of Edinburgh（爱丁堡大学）
Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and highly flexible model. We focus on alternative mixtures of GP experts, which model the joint distribution of the inputs and targets explicitly. We highlight issues of this approach in multi-dimensional input spaces, namely, poor scalability and the need for an unnecessarily large number of experts, degrading the predictive performance and increasing uncertainty. …
Dropout is a very effective method in preventing overfitting and has become the go-to regularizer for multi-layer neural networks in recent years. Hierarchical mixture of experts is a hierarchically gated model that defines a soft decision tree where leaves correspond to experts and decision nodes correspond to gating models that softly choose between its children, and as such, the model defines a soft hierarchical partitioning of the input space. In this work, we propose a variant of dropout for hierarchical mixture of experts that is faithful to the tree hierarchy defined by the model, as op…
Training large-scale mixture of experts models efficiently on modern hardware requires assigning datapoints in a batch to different experts, each with a limited capacity. Recently proposed assignment procedures lack a probabilistic interpretation and use biased estimators for training. As an alternative, we propose two unbiased estimators based on principled stochastic assignment procedures: one that skips datapoints which exceed expert capacity, and one that samples perfectly balanced assignments using an extension of the Gumbel-Matching distribution [29]. Both estimators are unbiased, as the…
Google, Inc.（谷歌公司）；Courant Institute, NYU（纽约大学库朗研究所）；Facebook AI Group（脸书人工智能团队）
Mixtures of Experts combine the outputs of several "expert" networks, each of which specializes in a different part of the input space. This is achieved by training a "gating" network that maps each input to a distribution over the experts. Such models show promise for building larger networks that are still cheap to compute at test time, and more parallelizable at training time. In this this work, we extend the Mixture of Experts to a stacked model, the Deep Mixture of Experts, with multiple sets of gating and experts. This exponentially increases the number of effective experts by associatin…
We develop a mixtures-of-experts (ME) approach to the multiclass classification where the predictors are univariate functions. It consists of a ME model in which both the gating network and the experts network are constructed upon multinomial logistic activation functions with functional inputs. We perform a regularized maximum likelihood estimation in which the coefficient functions enjoy interpretable sparsity constraints on targeted derivatives. We develop an EM-Lasso like algorithm to compute the regularized MLE and evaluate the proposed approach on simulated and real data.
TU Berlin（柏林工业大学）；SAP AI Research（SAP人工智能研究院）；University of Toronto（多伦多大学）；Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Machine learning systems are often deployed in domains that entail data from multiple modalities, for example, phenotypic and genotypic characteristics describe patients in healthcare. Previous works have developed multimodal variational autoencoders (VAEs) that generate several modalities. We consider subjective data, where single datapoints from one modality (such as class labels) describe multiple datapoints from another modality (such as images). We theoretically and empirically demonstrate that multimodal VAEs with a mixture of experts posterior can struggle to capture variability in such…
In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data, and strong local models are needed to make good predictions. Addressing these problems, we propose a binary tree-structured hierarchical routing mixture of experts (HRME) model that has classifiers as non-leaf node experts and simple regression models as leaf node experts. The c…
Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable model. Our approach relies on a low-rank linear regression to recover a symmetric tensor, which can be factorized into the parameters using a tensor power method. We prove rates of convergence for our estimator and provide an empirical evaluation illustrating its strengths relative t…
We propose a novel mixture-of-experts class to optimize computer vision models in accordance with data transfer limitations at test time. Our approach postulates that the minimum acceptable amount of data allowing for highly-accurate results can vary for different input space partitions. Therefore, we consider mixtures where experts require different amounts of data, and train a sparse gating function to divide the input space for each expert. By appropriate hyperparameter selection, our approach is able to bias mixtures of experts towards selecting specific experts over others. In this way, w…
IIIT Hyderabad（海得拉巴国际信息技术学院）；University of Hyderabad（海得拉巴大学）
fMRI semantic category understanding using linguistic encoding models attempt to learn a forward mapping that relates stimuli to the corresponding brain activation. Classical encoding models use linear multi-variate methods to predict the brain activation (all voxels) given the stimulus. However, these methods essentially assume multiple regions as one large uniform region or several independent regions, ignoring connections among them. In this paper, we present a mixture of experts-based model where a group of experts captures brain activity patterns related to particular regions of interest …
A useful strategy to deal with complex classification scenarios is the "divide and conquer" approach. The mixture of experts (MOE) technique makes use of this strategy by joinly training a set of classifiers, or experts, that are specialized in different regions of the input space. A global model, or gate function, complements the experts by learning a function that weights their relevance in different parts of the input space. Local feature selection appears as an attractive alternative to improve the specialization of experts and gate function, particularly, for the case of high dimensional …
University of California, Los Angeles（加州大学洛杉矶分校）；Carnegie Mellon University（卡内基梅隆大学）
The Mixture-of-Experts (MoE) layer, a sparsely-activated model controlled by a router, has achieved great success in deep learning. However, the understanding of such architecture remains elusive. In this paper, we formally study how the MoE layer improves the performance of neural network learning and why the mixture model will not collapse into a single model. Our empirical results suggest that the cluster structure of the underlying problem and the non-linearity of the expert are pivotal to the success of MoE. To further understand this, we consider a challenging classification problem with…
We present ScatterMoE, an implementation of Sparse Mixture-of-Experts (SMoE) on GPUs. ScatterMoE builds upon existing implementations, and overcoming some of the limitations to improve inference and training speed, and memory footprint. This implementation achieves this by avoiding padding and making excessive copies of the input. We introduce ParallelLinear, the main component we use to build our implementation and the various kernels used to speed up the operation. We benchmark our implementation against Megablocks, and show that it enables a higher throughput and lower memory footprint. We …
Sparsely Mixture of Experts (MoE) has received great interest due to its promising scaling capability with affordable computational overhead. MoE converts dense layers into sparse experts, and utilizes a gated routing network to make experts conditionally activated. However, as the number of experts grows, MoE with outrageous parameters suffers from overfitting and sparse data allocation. Such problems are especially severe on tasks with limited data, thus hindering the progress for MoE models to improve performance by scaling up. In this work, we propose Mixture of Expert Clusters - a general…
Department of Electrical Engineering and Automation（艾尔沃斯大学电气工程与自动化系）；Aalto University（艾尔沃斯大学）；School of Engineering Sciences（工程科学学院）；LUT University（卢托大学）；School of Mathematics（数学学院）；University of Edinburgh（爱丁堡大学）；Department of Mathematics（数学系）；University of Manchester（曼彻斯特大学）
Mixture-of-Clustered-Experts: Advancing Expert Specialization and Generalization in Instruction Tuning
Department of Computer Science and Engineering, Korea University, Republic of Korea（韩国大学计算机科学与工程系）；KT, Republic of Korea（韩国KT）；School of Software, Soongsil University, Republic of Korea（顺天大学软件学院）
Radboud University（拉德堡德大学）；Institute for Molecules and Materials（分子与材料研究所）
This work proposes a new data-driven model devised to integrate process knowledge into its structure to increase the human-machine synergy in the process industry. The proposed Contextual Mixture of Experts (cMoE) explicitly uses process knowledge along the model learning stage to mold the historical data to represent operators' context related to the process through possibility distributions. This model was evaluated in two real case studies for quality prediction, including a sulfur recovery unit and a polymerization process. The contextual mixture of experts was employed to represent differ…
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for efficient and massive parallelisation while keeping the memory consumption small. Given sufficient computing resources, our model can handle arbitrarily large data sets, without explicit sparse approximations. We provide strong experimental evidence that our model can be applied to lar…
ETH Zurich（苏黎世联邦理工学院）；Carnegie Mellon University（卡内基梅隆大学）
The Mixture of Experts architecture allows for outrageously large neural networks by scaling model parameter size independently from computational demand (FLOPs). However, current DNN frameworks cannot effectively support the dynamic data flow in Mixture of Experts, and implementations on top of these frameworks need to use workarounds that introduce significant overheads. To address the limitation of these frameworks, we present DynaMoE, a DNN library that uses dynamic recompilations to optimize and adapt the use of computational resources to the dynamic needs of Mixture of Experts models. Ou…
Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choic…
Let the Experts Speak: Improving Survival Prediction & Calibration via Mixture-of-Experts Heads
Department of Computer Science Columbia University USA（哥伦比亚大学计算机科学系）；Department of Computer Science New York University USA（纽约大学计算机科学系）；Department of Neurology Columbia University Medical Center USA（哥伦比亚大学医学中心神经病学系）；Department of Computer Science Barnard College USA（巴纳德学院计算机科学系）；Department of Biomedical Informatics Columbia University Medical Center USA（哥伦比亚大学医学中心生物医学信息学系）；NewYork-Presbyterian Hospital at Columbia University Medical Center USA（哥伦比亚大学医学中心新英格兰-纽约 Presbyterian 医院）
Beijing Institute of Technology（北京理工大学）；Microsoft Corporation（微软公司）；Peking University（北京大学）；Microsoft Research（微软研究院）
Sparse mixture of experts provides larger model capacity while requiring a constant computational overhead. It employs the routing mechanism to distribute input tokens to the best-matched experts according to their hidden representations. However, learning such a routing mechanism encourages token clustering around expert centroids, implying a trend toward representation collapse. In this work, we propose to estimate the routing scores between tokens and experts on a low-dimensional hypersphere. We conduct extensive experiments on cross-lingual language model pre-training and fine-tuning on do…
Tsinghua University（清华大学）；Institute for AI（人工智能研究院）；BNRist Center（北京信息科学与技术国家研究中心）；Tsinghua-Bosch Joint ML Center（清华-博世机器学习联合研究中心）；THBI Lab（清华脑与智能实验室）
We present Mixture of Contrastive Experts (MiCE), a unified probabilistic clustering framework that simultaneously exploits the discriminative representations learned by contrastive learning and the semantic structures captured by a latent mixture model. Motivated by the mixture of experts, MiCE employs a gating function to partition an unlabeled dataset into subsets according to the latent semantics and multiple experts to discriminate distinct subsets of instances assigned to them in a contrastive learning manner. To solve the nontrivial inference and learning problems caused by the latent v…
MC#: Mixture Compressor for Mixture-of-Experts Large Models
Department of Electrical and Electronic Engineering, The University of Hong Kong（香港大学电子与电气工程系）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）；NVIDIA Research（NVIDIA研究）
Many data have an underlying dependence on spatial location; it may be weather on the Earth, a simulation on a mesh, or a registered image. Yet this feature is rarely taken advantage of, and violates common assumptions made by many neural network layers, such as translation equivariance. Further, many works that do incorporate locality fail to capture fine-grained structure. To address this, we introduce the Spatial Mixture-of-Experts (SMoE) layer, a sparsely-gated layer that learns spatial structure in the input domain and routes experts at a fine-grained level to utilize it. We also develop …
Harvard University（哈佛大学）；Microsoft Research（微软研究院）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；University of Sienna（锡耶纳大学）
We propose Preferential MoE, a novel human-ML mixture-of-experts model that augments human expertise in decision making with a data-based classifier only when necessary for predictive performance. Our model exhibits an interpretable gating function that provides information on when human rules should be followed or avoided. The gating function is maximized for using human-based rules, and classification errors are minimized. We propose solving a coupled multi-objective problem with convex subproblems. We develop approximate algorithms and study their performance and convergence. Finally, we de…
