We examine the supervised learning problem in its continuous setting and give a general optimality condition through techniques of functional analysis and the calculus of variations. This enables us to solve the optimality condition for the desired function u numerically and make several comparisons with other widely utilized supervised learning models. We employ the accuracy and area under the receiver operating characteristic curve as metrics of the performance. Finally, 3 analyses are conducted based on these two mentioned metrics where we compare the models and make conclusions to determine whether or not our method is competitive.
This paper presents an infinite variational autoencoder (VAE) whose capacity adapts to suit the input data. This is achieved using a mixture model where the mixing coefficients are modeled by a Dirichlet process, allowing us to integrate over the coefficients when performing inference. Critically, this then allows us to automatically vary the number of autoencoders in the mixture based on the data. Experiments show the flexibility of our method, particularly for semi-supervised learning, where only a small number of training samples are available.
University of Amsterdam（阿姆斯特丹大学）；BrainCreators；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
Density estimation, compression and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models, called self-supervised Variational Auto-Encoder (selfVAE), that utilizes deterministic and discrete variational posteriors. This class of models allows to perform both conditional and unconditional sampling, while simplifying the objective function. First, we use a single self-supervised transformation as a latent variable, where a transformation is either dow…
In real-world applications, it is often expensive and time-consuming to obtain labeled examples. In such cases, knowledge transfer from related domains, where labels are abundant, could greatly reduce the need for extensive labeling efforts. In this scenario, transfer learning comes in hand. In this paper, we propose Deep Variational Transfer (DVT), a variational autoencoder that transfers knowledge across domains using a shared latent Gaussian mixture model. Thanks to the combination of a semi-supervised ELBO and parameters sharing across domains, we are able to simultaneously: (i) align all …
Semi-supervised learning is sought for leveraging the unlabelled data when labelled data is difficult or expensive to acquire. Deep generative models (e.g., Variational Autoencoder (VAE)) and semisupervised Generative Adversarial Networks (GANs) have recently shown promising performance in semi-supervised classification for the excellent discriminative representing ability. However, the latent code learned by the traditional VAE is not exclusive (repeatable) for a specific input sample, which prevents it from excellent classification performance. In particular, the learned latent representatio…
Texas A&M University（德州农工大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Semantic hashing has become a crucial component of fast similarity search in many large-scale information retrieval systems, in particular, for text data. Variational auto-encoders (VAEs) with binary latent variables as hashing codes provide state-of-the-art performance in terms of precision for document retrieval. We propose a pairwise loss function with discrete latent VAE to reward within-class similarity and between-class dissimilarity for supervised hashing. Instead of solving the optimization relying on existing biased gradient estimators, an unbiased low-variance gradient estimator is a…
The growth in the number of galaxy images is much faster than the speed at which these galaxies can be labelled by humans. However, by leveraging the information present in the ever growing set of unlabelled images, semi-supervised learning could be an effective way of reducing the required labelling and increasing classification accuracy. We develop a Variational Autoencoder (VAE) with Equivariant Transformer layers with a classifier network from the latent space. We show that this novel architecture leads to improvements in accuracy when used for the galaxy morphology classification task on …
We present a new flavor of Variational Autoencoder (VAE) that interpolates seamlessly between unsupervised, semi-supervised and fully supervised learning domains. We show that unlabeled datapoints not only boost unsupervised tasks, but also the classification performance. Vice versa, every label not only improves classification, but also unsupervised tasks. The proposed architecture is simple: A classification layer is connected to the topmost encoder layer, and then combined with the resampled latent layer for the decoder. The usual evidence lower bound (ELBO) loss is supplemented with a supe…
Carl-von-Ossietzky University of Oldenburg（奥尔登堡大学）；Frankfurt Institute for Advanced Studies (FIAS)（法兰克福高等研究院）；Goethe-University Frankfurt am Main（法兰克福歌德大学）
Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well performing generative networks for semi-supervised learning, we here combine two recent developments: a neural network reformulation of hierarchical Poisson mixtures (Neural Simpletrons), and a novel truncated variational EM approach (TV-EM). TV-EM provides theoretical guarantees for learning in generative networks, and its application to Neural Simpletrons…
Georgia Institute of Technology（佐治亚理工学院）；University of California, Berkeley（加州大学伯克利分校）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Most of the data-driven approaches applied to bearing fault diagnosis up to date are established in the supervised learning paradigm, which usually requires a large set of labeled data collected a priori. In practical applications, however, obtaining accurate labels based on real-time bearing conditions can be far more challenging than simply collecting a huge amount of unlabeled data using various sensors. In this paper, we thus propose a semi-supervised learning approach for bearing anomaly detection using variational autoencoder (VAE) based deep generative models, which allows for effective…
Department of Biomedical Informatics, University of Pittsburgh（匹兹堡大学生物医学信息学系）
Learning interpretable representations of data remains a central challenge in deep learning. When training a deep generative model, the observed data are often associated with certain categorical labels, and, in parallel with learning to regenerate data and simulate new data, learning an interpretable representation of each class of data is also a process of acquiring knowledge. Here, we present a novel generative model, referred to as the Supervised Vector Quantized Variational AutoEncoder (S-VQ-VAE), which combines the power of supervised and unsupervised learning to obtain a unique, interpr…
Imperial College London（帝国理工学院）；Bogazici University（海峡大学）
We present the development of a semi-supervised regression method using variational autoencoders (VAE), which is customized for use in soft sensing applications. We motivate the use of semi-supervised learning considering the fact that process quality variables are not collected at the same frequency as other process variables leading to many unlabelled records in operational datasets. These unlabelled records are not possible to use for training quality variable predictions based on supervised learning methods. Use of VAEs for unsupervised learning is well established and recently they were u…
Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF is most often utilized as an unsupervised feature extractor followed by classification in the obtained feature subspace. Having mapped the class labels to a more general concept of groups which underlie sparsity of the coefficients, what the proposed group sparse NMF model allows…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Institute for Artificial Intelligence, KAIST（韩国科学技术院人工智能研究所）
We aim to separate the generative factors of data into two latent vectors in a variational autoencoder. One vector captures class factors relevant to target classification tasks, while the other vector captures style factors relevant to the remaining information. To learn the discrete class features, we introduce supervision using a small amount of labeled data, which can simply yet effectively reduce the effort required for hyperparameter tuning performed in existing unsupervised methods. Furthermore, we introduce a learning objective to encourage statistical independence between the vectors.…
In this work we introduce a semi-supervised approach to the voice conversion problem, in which speech from a source speaker is converted into speech of a target speaker. The proposed method makes use of both parallel and non-parallel utterances from the source and target simultaneously during training. This approach can be used to extend existing parallel data voice conversion systems such that they can be trained with semi-supervision. We show that incorporating semi-supervision improves the voice conversion performance compared to fully supervised training when the number of parallel utteran…
Recently, variational autoencoders have been successfully used to learn a probabilistic prior over speech signals, which is then used to perform speech enhancement. However, variational autoencoders are trained on clean speech only, which results in a limited ability of extracting the speech signal from noisy speech compared to supervised approaches. In this paper, we propose to guide the variational autoencoder with a supervised classifier separately trained on noisy speech. The estimated label is a high-level categorical variable describing the speech signal (e.g. speech activity) allowing f…
Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$). In the case where the codomain has known structure, a large unfeatured dataset ($\mathbf{y}$) is potentially available. We develop a parameter-efficient, deep semi-supervised generative model for the purpose of exploiting this untapped data source. Empirical results show improved performance in disentangling latent variable semantics as well as improved discriminative prediction on Martian spectr…
NTT Secure Platform Laboratories（NTT安全平台实验室）；NTT Communication Science Laboratories（NTT通信科学实验室）；NTT Software Innovation Center（NTT软件创新中心）
We propose the Autoencoding Binary Classifiers (ABC), a novel supervised anomaly detector based on the Autoencoder (AE). There are two main approaches in anomaly detection: supervised and unsupervised. The supervised approach accurately detects the known anomalies included in training data, but it cannot detect the unknown anomalies. Meanwhile, the unsupervised approach can detect both known and unknown anomalies that are located away from normal data points. However, it does not detect known anomalies as accurately as the supervised approach. Furthermore, even if we have labeled normal data p…
East China Normal University（华东师范大学）；Microsoft Research Asia（微软亚洲研究院）
Generative graph self-supervised learning (SSL) aims to learn node representations by reconstructing the input graph data. However, most existing methods focus on unsupervised learning tasks only and very few work has shown its superiority over the state-of-the-art graph contrastive learning (GCL) models, especially on the classification task. While a very recent model has been proposed to bridge the gap, its performance on unsupervised learning tasks is still unknown. In this paper, to comprehensively enhance the performance of generative graph SSL against other GCL models on both unsupervise…
Labeled sequence transduction is a task of transforming one sequence into another sequence that satisfies desiderata specified by a set of labels. In this paper we propose multi-space variational encoder-decoders, a new model for labeled sequence transduction with semi-supervised learning. The generative model can use neural networks to handle both discrete and continuous latent variables to exploit various features of data. Experiments show that our model provides not only a powerful supervised framework but also can effectively take advantage of the unlabeled data. On the SIGMORPHON morpholo…
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for supervised learning problem. This formulation circumvents the difficulty of imposing the constraints of given values on isolated data points in continuum modelling. Under a necessary and sufficient condition within our unified framework, we establish the well-posedness of the Fourier-domain variational problem, by showing a critical exponent depending on the data d…
Neural Network based controllers hold enormous potential to learn complex, high-dimensional functions. However, they are prone to overfitting and unwarranted extrapolations. PAC Bayes is a generalized framework which is more resistant to overfitting and that yields performance bounds that hold with arbitrarily high probability even on the unjustified extrapolations. However, optimizing to learn such a function and a bound is intractable for complex tasks. In this work, we propose a method to simultaneously learn such a function and estimate performance bounds that scale organically to high-dim…
Although semi-supervised variational autoencoder (SemiVAE) works in image classification task, it fails in text classification task if using vanilla LSTM as its decoder. From a perspective of reinforcement learning, it is verified that the decoder's capability to distinguish between different categorical labels is essential. Therefore, Semi-supervised Sequential Variational Autoencoder (SSVAE) is proposed, which increases the capability by feeding label into its decoder RNN at each time-step. Two specific decoder structures are investigated and both of them are verified to be effective. Beside…
We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straightforward and fast; using well-known auxiliary variables for…
In anomaly detection (AD), one seeks to identify whether a test sample is abnormal, given a data set of normal samples. A recent and promising approach to AD relies on deep generative models, such as variational autoencoders (VAEs), for unsupervised learning of the normal data distribution. In semi-supervised AD (SSAD), the data also includes a small sample of labeled anomalies. In this work, we propose two variational methods for training VAEs for SSAD. The intuitive idea in both methods is to train the encoder to `separate' between latent vectors for normal and outlier data. We show that thi…
In this paper we address the problem of enhancing speech signals in noisy mixtures using a source separation approach. We explore the use of neural networks as an alternative to a popular speech variance model based on supervised non-negative matrix factorization (NMF). More precisely, we use a variational autoencoder as a speaker-independent supervised generative speech model, highlighting the conceptual similarities that this approach shares with its NMF-based counterpart. In order to be free of generalization issues regarding the noisy recording environments, we follow the approach of havin…
Applied Artificial Intelligence Institute (A2I2), Deakin University（应用人工智能研究所（A2I2），迪肯大学）
We propose two generic methods for improving semi-supervised learning (SSL). The first integrates weight perturbation (WP) into existing "consistency regularization" (CR) based methods. We implement WP by leveraging variational Bayesian inference (VBI). The second method proposes a novel consistency loss called "maximum uncertainty regularization" (MUR). While most consistency losses act on perturbations in the vicinity of each data point, MUR actively searches for "virtual" points situated beyond this region that cause the most uncertain class predictions. This allows MUR to impose smoothness…
Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；Paul G. Allen School of Computer Science & Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）；Carnegie Mellon University（卡内基梅隆大学）
We introduce VAMPIRE, a lightweight pretraining framework for effective text classification when data and computing resources are limited. We pretrain a unigram document model as a variational autoencoder on in-domain, unlabeled data and use its internal states as features in a downstream classifier. Empirically, we show the relative strength of VAMPIRE against computationally expensive contextual embeddings and other popular semi-supervised baselines under low resource settings. We also find that fine-tuning to in-domain data is crucial to achieving decent performance from contextual embeddin…
Binary Stochastic Filtering (BSF), the algorithm for feature selection and neuron pruning is proposed in this work. The method defines filtering layer which penalizes amount of the information involved in the training process. This information could be the input data or output of the previous layer, which directly leads to the feature selection or neuron pruning respectively, producing \textit{ad hoc} subset of features or selecting optimal number of neurons in each layer. Filtering layer stochastically passes or drops features based on individual weights, which are tuned with standard backpro…
Product reviews and ratings on e-commerce websites provide customers with detailed insights about various aspects of the product such as quality, usefulness, etc. Since they influence customers' buying decisions, product reviews have become a fertile ground for abuse by sellers (colluding with reviewers) to promote their own products or to tarnish the reputation of competitor's products. In this paper, our focus is on detecting such abusive entities (both sellers and reviewers) by applying tensor decomposition on the product reviews data. While tensor decomposition is mostly unsupervised, we f…
Molecular Representation Learning is essential to solving many drug discovery and computational chemistry problems. It is a challenging problem due to the complex structure of molecules and the vast chemical space. Graph representations of molecules are more expressive than traditional representations, such as molecular fingerprints. Therefore, they can improve the performance of machine learning models. We propose SeMole, a method that augments the Junction Tree Variational Autoencoders, a state-of-the-art generative model for molecular graphs, with semi-supervised learning. SeMole aims to im…
Discrete latent variables are considered important for real world data, which has motivated research on Variational Autoencoders (VAEs) with discrete latents. However, standard VAE training is not possible in this case, which has motivated different strategies to manipulate discrete distributions in order to train discrete VAEs similarly to conventional ones. Here we ask if it is also possible to keep the discrete nature of the latents fully intact by applying a direct discrete optimization for the encoding model. The approach is consequently strongly diverting from standard VAE-training by si…
Northwestern Polytechnical University（西北工业大学）；Pennsylvania State University（宾夕法尼亚州立大学）；Nanyang Technological University（南洋理工大学）
Semi-supervised learning is attracting increasing attention due to the fact that datasets of many domains lack enough labeled data. Variational Auto-Encoder (VAE), in particular, has demonstrated the benefits of semi-supervised learning. The majority of existing semi-supervised VAEs utilize a classifier to exploit label information, where the parameters of the classifier are introduced to the VAE. Given the limited labeled data, learning the parameters for the classifiers may not be an optimal solution for exploiting label information. Therefore, in this paper, we develop a novel approach for …
A new method for learning variational autoencoders (VAEs) is developed, based on Stein variational gradient descent. A key advantage of this approach is that one need not make parametric assumptions about the form of the encoder distribution. Performance is further enhanced by integrating the proposed encoder with importance sampling. Excellent performance is demonstrated across multiple unsupervised and semi-supervised problems, including semi-supervised analysis of the ImageNet data, demonstrating the scalability of the model to large datasets.
School of Computing and Information Systems（计算与信息系统学院）；The University of Melbourne（墨尔本大学）
Supervised models of NLP rely on large collections of text which closely resemble the intended testing setting. Unfortunately matching text is often not available in sufficient quantity, and moreover, within any domain of text, data is often highly heterogenous. In this paper we propose a method to distill the important domain signal as part of a multi-domain learning system, using a latent variable model in which parts of a neural model are stochastically gated based on the inferred domain. We compare the use of discrete versus continuous latent variables, operating in a domain-supervised or …
While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for learning the latent space of imaging data and performing supervised regression. Based on recent advances in learning disentangled representations, the novel generative process explicitly models the conditional distribution of latent representations with respect to the regression target variable. Performing a variational inference procedure on this model leads to j…
University of Virginia（弗吉尼亚大学）；The George Washington University（乔治华盛顿大学）
This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fast computational model providing fuzzy logic and supervised learning is one of the main challenges in the machine learning. In this research paper, we present FSL-BM algorithm as an efficient solution of supervised learning with fuzzy logic processing using binary meta-feature re…
LIPN（巴黎第十三大学计算机科学实验室）；Université Sorbonne Paris Nord（索邦巴黎北大学）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）
Even though Variational Autoencoders (VAEs) are widely used for semi-supervised learning, the reason why they work remains unclear. In fact, the addition of the unsupervised objective is most often vaguely described as a regularization. The strength of this regularization is controlled by down-weighting the objective on the unlabeled part of the training set. Through an analysis of the objective of semi-supervised VAEs, we observe that they use the posterior of the learned generative model to guide the inference model in learning the partially observed latent variable. We show that given this …
We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing unit. We describe how to do supervised, unsupervised and semi-supervised learning, and nominal and ordinal classification, with the model. We analyze generative properties of the approach, and the classification effectiveness under nominal and ordinal classification, using two benchmark datasets. Our results show that our model can achieve comparable results…
This paper describes a statistically-principled semi-supervised method of automatic chord estimation (ACE) that can make effective use of music signals regardless of the availability of chord annotations. The typical approach to ACE is to train a deep classification model (neural chord estimator) in a supervised manner by using only annotated music signals. In this discriminative approach, prior knowledge about chord label sequences (model output) has scarcely been taken into account. In contrast, we propose a unified generative and discriminative approach in the framework of amortized variati…
Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark（丹麦技术大学诺和诺德基金会生物可持续性中心）；University of Copenhagen（哥本哈根大学）
Multimodal generative models should be able to learn a meaningful latent representation that enables a coherent joint generation of all modalities (e.g., images and text). Many applications also require the ability to accurately sample modalities conditioned on observations of a subset of the modalities. Often not all modalities may be observed for all training data points, so semi-supervised learning should be possible. In this study, we propose a novel product-of-experts (PoE) based variational autoencoder that have these desired properties. We benchmark it against a mixture-of-experts (MoE)…
University of Edinburgh（爱丁堡大学）；University of Amsterdam（阿姆斯特丹大学）
Human annotation for syntactic parsing is expensive, and large resources are available only for a fraction of languages. A question we ask is whether one can leverage abundant unlabeled texts to improve syntactic parsers, beyond just using the texts to obtain more generalisable lexical features (i.e. beyond word embeddings). To this end, we propose a novel latent-variable generative model for semi-supervised syntactic dependency parsing. As exact inference is intractable, we introduce a differentiable relaxation to obtain approximate samples and compute gradients with respect to the parser par…
The unsupervised training of GANs and VAEs has enabled them to generate realistic images mimicking real-world distributions and perform image-based unsupervised clustering or semi-supervised classification. Combining the power of these two generative models, we introduce Multi-Adversarial Variational autoEncoder Networks (MAVENs), a novel network architecture that incorporates an ensemble of discriminators in a VAE-GAN network, with simultaneous adversarial learning and variational inference. We apply MAVENs to the generation of synthetic images and propose a new distribution measure to quanti…
Tsinghua University（清华大学）；Microsoft Research Asia（微软亚洲研究院）
Adversarial learning is a widely used technique in fair representation learning to remove the biases on sensitive attributes from data representations. It usually requires to incorporate the sensitive attribute labels as prediction targets. However, in many scenarios the sensitive attribute labels of many samples can be unknown, and it is difficult to train a strong discriminator based on the scarce data with observed attribute labels, which may lead to generate unfair representations. In this paper, we propose a semi-supervised fair representation learning approach based on adversarial variat…
Disentangled representations have recently been shown to improve fairness, data efficiency and generalisation in simple supervised and reinforcement learning tasks. To extend the benefits of disentangled representations to more complex domains and practical applications, it is important to enable hyperparameter tuning and model selection of existing unsupervised approaches without requiring access to ground truth attribute labels, which are not available for most datasets. This paper addresses this problem by introducing a simple yet robust and reliable method for unsupervised disentangled mod…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Nanyang Technological University（南洋理工大学）；Xidian University（西安电子科技大学）
Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level and graph-level classification tasks. However, GNNs typically treat the graph structure as given and ignore how the edges are formed. This paper introduces a graph generative process to model how the observed edges are generated by aggregating the node interactions over a set of overlapping node communities, each of which contributes to the edges via a logica…
Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；The University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
The increasing amount of data in astronomy provides great challenges for machine learning research. Previously, supervised learning methods achieved satisfactory recognition accuracy for the star-galaxy classification task, based on manually labeled data set. In this work, we propose a novel unsupervised approach for the star-galaxy recognition task, namely Cascade Variational Auto-Encoder (CasVAE). Our empirical results show our method outperforms the baseline model in both accuracy and stability.
Ulm University（乌尔姆大学）；Institute of Neural Information Processing（神经信息处理研究所）
One weakness of machine learning algorithms is the poor ability of models to solve new problems without forgetting previously acquired knowledge. The Continual Learning (CL) paradigm has emerged as a protocol to systematically investigate settings where the model sequentially observes samples generated by a series of tasks. In this work, we take a task-agnostic view of continual learning and develop a hierarchical information-theoretic optimality principle that facilitates a trade-off between learning and forgetting. We discuss this principle from a Bayesian perspective and show its connection…
Out-of-distribution (OOD) detection, i.e., finding test samples derived from a different distribution than the training set, as well as reasoning about such samples (OOD reasoning), are necessary to ensure the safety of results generated by machine learning models. Recently there have been promising results for OOD detection in the latent space of variational autoencoders (VAEs). However, without disentanglement, VAEs cannot perform OOD reasoning. Disentanglement ensures a one- to-many mapping between generative factors of OOD (e.g., rain in image data) and the latent variables to which they a…
Thakur Institute Of Management Studies, Career Development & Research（塔库尔管理研究、职业发展与研究学院）；University of Mumbai（孟买大学）
High dimensional data for classification does create many difficulties for machine learning algorithms. The generalization can be done using ensemble learning methods such as bagging based supervised non-parametric random forest algorithm. In this paper we solve the problem of binary classification for high dimensional data using random forest for polycystic ovary syndrome dataset. We have performed the implementation and provided a detailed visualization of the data for general inference. The training accuracy that we have achieved is 95.6% and validation accuracy over 91.74% respectively.
