اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMultivariate Density Estimation with Deep Neural Mixture Models
117
0
0.0
(
0
)
تأليف
Edmondo Trentin
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorovs axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorovs axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.
قيم البحث
اقرأ أيضاً
Significant computational cost and memory requirements for deep neural networks (DNNs) make it difficult to utilize DNNs in resource-constrained environments. Binary neural network (BNN), which uses binary weights and binary activations, has been gai
ning interests for its hardware-friendly characteristics and minimal resource requirement. However, BNN usually suffers from accuracy degradation. In this paper, we introduce BitSplit-Net, a neural network which maintains the hardware-friendly characteristics of BNN while improving accuracy by using multi-bit precision. In BitSplit-Net, each bit of multi-bit activations propagates independently throughout the network before being merged at the end of the network. Thus, each bit path of the BitSplit-Net resembles BNN and hardware friendly features of BNN, such as bitwise binary activation function, are preserved in our scheme. We demonstrate that the BitSplit version of LeNet-5, VGG-9, AlexNet, and ResNet-18 can be trained to have similar classification accuracy at a lower computational cost compared to conventional multi-bit networks with low bit precision (<= 4-bit). We further evaluate BitSplit-Net on GPU with custom CUDA kernel, showing that BitSplit-Net can achieve better hardware performance in comparison to conventional multi-bit networks.
Computation using brain-inspired spiking neural networks (SNNs) with neuromorphic hardware may offer orders of magnitude higher energy efficiency compared to the current analog neural networks (ANNs). Unfortunately, training SNNs with the same number
of layers as state of the art ANNs remains a challenge. To our knowledge the only method which is successful in this regard is supervised training of ANN and then converting it to SNN. In this work we directly train deep SNNs using backpropagation with surrogate gradient and find that due to implicitly recurrent nature of feed forward SNNs the exploding or vanishing gradient problem severely hinders their training. We show that this problem can be solved by tuning the surrogate gradient function. We also propose using batch normalization from ANN literature on input currents of SNN neurons. Using these improvements we show that is is possible to train SNN with ResNet50 architecture on CIFAR100 and Imagenette object recognition datasets. The trained SNN falls behind in accuracy compared to analogous ANN but requires several orders of magnitude less inference time steps (as low as 10) to reach good accuracy compared to SNNs obtained by conversion from ANN which require on the order of 1000 time steps.
Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in 2D sensor
readings, or reconstructing scenes from 3D scans. In this paper, we introduce a learned, data-driven deep density estimation (DDE) to infer PDFs in an accurate and efficient manner, while being independent of domain dimensionality or sample size. Furthermore, we do not require access to the original PDF during estimation, neither in parametric form, nor as priors, or in the form of many samples. This is enabled by training an unstructured convolutional neural network on an infinite stream of synthetic PDFs, as unbound amounts of synthetic training data generalize better across a deck of natural PDFs than any natural finite training data will do. Thus, we hope that our publicly available DDE method will be beneficial in many areas of data analysis, where continuous models are to be estimated from discrete observations.
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a low
er-dimensional manifold of high probability. It has been more difficult, however, to exploit this insight to build explicit, tractable density models for high-dimensional data. In this paper, we introduce the deep density model (DDM), a new approach to density estimation. We exploit insights from deep learning to construct a bijective map to a representation space, under which the transformation of the distribution of the data is approximately factorized and has identical and known marginal densities. The simplicity of the latent distribution under the model allows us to feasibly explore it, and the invertibility of the map to characterize contraction of measure across it. This enables us to compute normalized densities for out-of-sample data. This combination of tractability and flexibility allows us to tackle a variety of probabilistic tasks on high-dimensional datasets, including: rapid computation of normalized densities at test-time without evaluating a partition function; generation of samples without MCMC; and characterization of the joint entropy of the data.
Deep neural networks and decision trees operate on largely separate paradigms; typically, the former performs representation learning with pre-specified architectures, while the latter is characterised by learning hierarchies over pre-specified featu
res with data-driven architectures. We unite the two via adaptive neural trees (ANTs) that incorporates representation learning into edges, routing functions and leaf nodes of a decision tree, along with a backpropagation-based training algorithm that adaptively grows the architecture from primitive modules (e.g., convolutional layers). We demonstrate that, whilst achieving competitive performance on classification and regression datasets, ANTs benefit from (i) lightweight inference via conditional computation, (ii) hierarchical separation of features useful to the task e.g. learning meaningful class associations, such as separating natural vs. man-made objects, and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
