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We provide a comprehensive theory of conducting in-sample statistical inference about receiver operating characteristic (ROC) curves that are based on predicted values from a first stage model with estimated parameters (such as a logit regression). The term "in-sample" refers to the practice of using the same data for model estimation (training) and subsequent evaluation, i.e., the construction of the ROC curve. We show that in this case the first stage estimation error has a generally non-negligible impact on the asymptotic distribution of the ROC curve and develop the appropriate pointwise and functional limit theory. We propose methods for simulating the distribution of the limit process and show how to use the results in practice in comparing ROC curves.

Bayesian supervised predictive classifiers, hypothesis testing, and parametric estimation under Partition Exchangeability are implemented. The two classifiers presented are the marginal classifier (that assumes test data is i.i.d.) next to a more computationally costly but accurate simultaneous classifier (that finds a labelling for the entire test dataset at once based on simultanous use of all the test data to predict each label). We also provide the Maximum Likelihood Estimation (MLE) of the only underlying parameter of the partition exchangeability generative model as well as hypothesis testing statistics for equality of this parameter with a single value, alternative, or multiple samples. We present functions to simulate the sequences from Ewens Sampling Formula as the realisation of the Poisson-Dirichlet distribution and their respective probabilities.

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}.

Computational design problems arise in a number of settings, from synthetic biology to computer architectures. In this paper, we aim to solve data-driven model-based optimization (MBO) problems, where the goal is to find a design input that maximizes an unknown objective function provided access to only a static dataset of prior experiments. Such data-driven optimization procedures are the only practical methods in many real-world domains where active data collection is expensive (e.g., when optimizing over proteins) or dangerous (e.g., when optimizing over aircraft designs). Typical methods for MBO that optimize the design against a learned model suffer from distributional shift: it is easy to find a design that "fools" the model into predicting a high value. To overcome this, we propose conservative objective models (COMs), 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, and uses it for optimization. Structurally, COMs resemble adversarial training methods used to overcome adversarial examples. COMs are simple to implement and outperform a number of existing methods on a wide range of MBO problems, including optimizing protein sequences, robot morphologies, neural network weights, and superconducting materials.

This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.

Meta-reinforcement learning (meta-RL) aims to learn from multiple training tasks the ability to adapt efficiently to unseen test tasks. Despite the success, existing meta-RL algorithms are known to be sensitive to the task distribution shift. When the test task distribution is different from the training task distribution, the performance may degrade significantly. To address this issue, this paper proposes Model-based Adversarial Meta-Reinforcement Learning (AdMRL), where we aim to minimize the worst-case sub-optimality gap -- the difference between the optimal return and the return that the algorithm achieves after adaptation -- across all tasks in a family of tasks, with a model-based approach. We propose a minimax objective and optimize it by alternating between learning the dynamics model on a fixed task and finding the adversarial task for the current model -- the task for which the policy induced by the model is maximally suboptimal. Assuming the family of tasks is parameterized, we derive a formula for the gradient of the suboptimality with respect to the task parameters via the implicit function theorem, and show how the gradient estimator can be efficiently implemented by the conjugate gradient method and a novel use of the REINFORCE estimator. We evaluate our approach on several continuous control benchmarks and demonstrate its efficacy in the worst-case performance over all tasks, the generalization power to out-of-distribution tasks, and in training and test time sample efficiency, over existing state-of-the-art meta-RL algorithms.

Fine-tuning a deep network trained with the standard cross-entropy loss is a strong baseline for few-shot learning. When fine-tuned transductively, this outperforms the current state-of-the-art on standard datasets such as Mini-ImageNet, Tiered-ImageNet, CIFAR-FS and FC-100 with the same hyper-parameters. The simplicity of this approach enables us to demonstrate the first few-shot learning results on the ImageNet-21k dataset. We find that using a large number of meta-training classes results in high few-shot accuracies even for a large number of few-shot classes. We do not advocate our approach as the solution for few-shot learning, but simply use the results to highlight limitations of current benchmarks and few-shot protocols. We perform extensive studies on benchmark datasets to propose a metric that quantifies the "hardness" of a few-shot episode. This metric can be used to report the performance of few-shot algorithms in a more systematic way.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in the embedding space has been used to improve the performance of several DDML methods. However, the commonly used Euclidean distance is no longer an accurate metric for $L2$-normalized embedding space, i.e., a hyper-sphere. Another challenge of current DDML methods is that their loss functions are usually based on rigid data formats, such as the triplet tuple. Thus, an extra process is needed to prepare data in specific formats. In addition, their losses are obtained from a limited number of samples, which leads to a lack of the global view of the embedding space. In this paper, we replace the Euclidean distance with the cosine similarity to better utilize the $L2$-normalization, which is able to attenuate the curse of dimensionality. More specifically, a novel loss function based on the von Mises-Fisher distribution is proposed to learn a compact hyper-spherical embedding space. Moreover, a new efficient learning algorithm is developed to better capture the global structure of the embedding space. Experiments for both classification and retrieval tasks on several standard datasets show that our method achieves state-of-the-art performance with a simpler training procedure. Furthermore, we demonstrate that, even with a small number of convolutional layers, our model can still obtain significantly better classification performance than the widely used softmax loss.