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In federated learning, a strong global model is collaboratively learned by aggregating clients' locally trained models. Although this precludes the need to access clients' data directly, the global model's convergence often suffers from data heterogeneity. This study starts from an analogy to continual learning and suggests that forgetting could be the bottleneck of federated learning. We observe that the global model forgets the knowledge from previous rounds, and the local training induces forgetting the knowledge outside of the local distribution. Based on our findings, we hypothesize that tackling down forgetting will relieve the data heterogeneity problem. To this end, we propose a novel and effective algorithm, Federated Not-True Distillation (FedNTD), which preserves the global perspective on locally available data only for the not-true classes. In the experiments, FedNTD shows state-of-the-art performance on various setups without compromising data privacy or incurring additional communication costs.

Computational analysis methods including machine learning have a significant impact in the fields of genomics and medicine. High-throughput gene expression analysis methods such as microarray technology and RNA sequencing produce enormous amounts of data. Traditionally, statistical methods are used for comparative analysis of the gene expression data. However, more complex analysis for classification and discovery of feature genes or sample observations requires sophisticated computational approaches. In this review, we compile various statistical and computational tools used in analysis of expression microarray data. Even though, the methods are discussed in the context of expression microarray data, they can also be applied for the analysis of RNA sequencing or quantitative proteomics datasets. We specifically discuss methods for missing value (gene expression) imputation, feature gene scaling, selection and extraction of features for dimensionality reduction, and learning and analysis of expression data. We discuss the types of missing values and the methods and approaches usually employed in their imputation. We also discuss methods of data transformation and feature scaling viz. normalization and standardization. Various approaches used in feature selection and extraction are also reviewed. Lastly, learning and analysis methods including class comparison, class prediction, and class discovery along with their evaluation parameters are described in detail. We have described the process of generation of a microarray gene expression data along with advantages and limitations of the above-mentioned techniques. We believe that this detailed review will help the users to select appropriate methods based on the type of data and the expected outcome.

Medical tasks are prone to inter-rater variability due to multiple factors such as image quality, professional experience and training, or guideline clarity. Training deep learning networks with annotations from multiple raters is a common practice that mitigates the model's bias towards a single expert. Reliable models generating calibrated outputs and reflecting the inter-rater disagreement are key to the integration of artificial intelligence in clinical practice. Various methods exist to take into account different expert labels. We focus on comparing three label fusion methods: STAPLE, average of the rater's segmentation, and random sampling each rater's segmentation during training. Each label fusion method is studied using the conventional training framework or the recently published SoftSeg framework that limits information loss by treating the segmentation task as a regression. Our results, across 10 data splittings on two public datasets, indicate that SoftSeg models, regardless of the ground truth fusion method, had better calibration and preservation of the inter-rater rater variability compared with their conventional counterparts without impacting the segmentation performance. Conventional models, i.e., trained with a Dice loss, with binary inputs, and sigmoid/softmax final activate, were overconfident and underestimated the uncertainty associated with inter-rater variability. Conversely, fusing labels by averaging with the SoftSeg framework led to underconfident outputs and overestimation of the rater disagreement. In terms of segmentation performance, the best label fusion method was different for the two datasets studied, indicating this parameter might be task-dependent. However, SoftSeg had segmentation performance systematically superior or equal to the conventionally trained models and had the best calibration and preservation of the inter-rater variability.

Computational analysis methods including machine learning have a significant impact in the fields of genomics and medicine. High-throughput gene expression analysis methods such as microarray technology and RNA sequencing produce enormous amounts of data. Traditionally, statistical methods are used for comparative analysis of the gene expression data. However, more complex analysis for classification and discovery of feature genes or sample observations requires sophisticated computational approaches. In this review, we compile various statistical and computational tools used in analysis of expression microarray data. Even though, the methods are discussed in the context of expression microarray data, they can also be applied for the analysis of RNA sequencing or quantitative proteomics datasets. We specifically discuss methods for missing value (gene expression) imputation, feature gene scaling, selection and extraction of features for dimensionality reduction, and learning and analysis of expression data. We discuss the types of missing values and the methods and approaches usually employed in their imputation. We also discuss methods of data transformation and feature scaling viz. normalization and standardization. Various approaches used in feature selection and extraction are also reviewed. Lastly, learning and analysis methods including class comparison, class prediction, and class discovery along with their evaluation parameters are described in detail. We have described the process of generation of a microarray gene expression data along with advantages and limitations of the above-mentioned techniques. We believe that this detailed review will help the users to select appropriate methods based on the type of data and the expected outcome.

We consider a special case of bandit problems, named batched bandits, in which an agent observes batches of responses over a certain time period. Unlike previous work, we consider a practically relevant batch-centric scenario of batch learning. That is to say, we provide a policy-agnostic regret analysis and demonstrate upper and lower bounds for the regret of a candidate policy. Our main theoretical results show that the impact of batch learning can be measured proportional to the regret of online behavior. Primarily, we study two settings of the problem: instance-independent and instance-dependent. While the upper bound is the same for both settings, the worst-case lower bound is more comprehensive in the former case and more accurate in the latter one. Also, we provide a more robust result for the 2-armed bandit problem as an important insight. Finally, we demonstrate the consistency of theoretical results by conducting empirical experiments and reflect on the optimal batch size choice.

It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first part of the paper 13 model based procedures are compared to the model-free Gaussian covariate procedure in terms of the covariates selected and the time required. The comparison is based on four data sets and two simulations. There is nothing special about these data sets which are often used as examples in the literature. All the model based procedures failed. In the second part of the paper it is argued that the cause of this failure is the very use of a model. If the model involves all the available covariates standard P-values can be used. The use of P-values in this situation is quite straightforward. As soon as the model specifies only some unknown subset of the covariates the problem being to identify this subset the situation changes radically. There are many P-values, they are dependent and most of them are invalid. The Bayesian paradigm also assumes a correct model but although there are no conceptual problems with a large number of covariates there is a considerable overhead causing computational and allocation problems even for moderately sized data sets. The Gaussian covariate procedure is based on P-values which are defined as the probability that a random Gaussian covariate is better than the covariate being considered. These P-values are exact and valid whatever the situation. The allocation requirements and the algorithmic complexity are both linear in the size of the data making the procedure capable of handling large data sets. It outperforms all the other procedures in every respect.

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{//github.com/shivram1987/ActivationFunctions}.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.

The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures and under varying constraints. In this paper we focus on the exclusive row biclustering problem for gene expression data sets, in which each row can only be a member of a single bicluster while columns can participate in multiple ones. This type of biclustering may be adequate, for example, for clustering groups of cancer patients where each patient (row) is expected to be carrying only a single type of cancer, while each cancer type is associated with multiple (and possibly overlapping) genes (columns). We present a novel method to identify these exclusive row biclusters through a combination of existing biclustering algorithms and combinatorial auction techniques. We devise an approach for tuning the threshold for our algorithm based on comparison to a null model in the spirit of the Gap statistic approach. We demonstrate our approach on both synthetic and real-world gene expression data and show its power in identifying large span non-overlapping rows sub matrices, while considering their unique nature. The Gap statistic approach succeeds in identifying appropriate thresholds in all our examples.