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Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. Importantly, the main aim in theory works on the subject is to understand the extent to which convergence rates -- in learning a common representation -- \emph{may scale with the number $N$ of tasks} (as well as the number of samples per task). First steps in this setting demonstrate this property when both the shared representation amongst tasks, and task-specific regression functions, are linear. This linear setting readily reveals the benefits of aggregating tasks, e.g., via averaging arguments. In practice, however, the representation is often highly nonlinear, introducing nontrivial biases in each task that cannot easily be averaged out as in the linear case. In the present work, we derive theoretical guarantees for meta-learning with nonlinear representations. In particular, assuming the shared nonlinearity maps to an infinite-dimensional RKHS, we show that additional biases can be mitigated with careful regularization that leverages the smoothness of task-specific regression functions,

Aspect sentiment quad prediction (ASQP) aims to predict the quad sentiment elements for a given sentence, which is a critical task in the field of aspect-based sentiment analysis. However, the data imbalance issue has not received sufficient attention in ASQP task. In this paper, we divide the issue into two-folds, quad-pattern imbalance and aspect-category imbalance, and propose an Adaptive Data Augmentation (ADA) framework to tackle the imbalance issue. Specifically, a data augmentation process with a condition function adaptively enhances the tail quad patterns and aspect categories, alleviating the data imbalance in ASQP. Following previous studies, we also further explore the generative framework for extracting complete quads by introducing the category prior knowledge and syntax-guided decoding target. Experimental results demonstrate that data augmentation for imbalance in ASQP task can improve the performance, and the proposed ADA method is superior to naive data oversampling.

A recurring challenge in the application of redistricting simulation algorithms lies in extracting useful summaries and comparisons from a large ensemble of districting plans. Researchers often compute summary statistics for each district in a plan, and then study their distribution across the plans in the ensemble. This approach discards rich geographic information that is inherent in districting plans. We introduce the projective average, an operation that projects a district-level summary statistic back to the underlying geography and then averages this statistic across plans in the ensemble. Compared to traditional district-level summaries, projective averages are a powerful tool for geographically granular, sub-district analysis of districting plans along a variety of dimensions. However, care must be taken to account for variation within redistricting ensembles, to avoid misleading conclusions. We propose and validate a multiple-testing procedure to control the probability of incorrectly identifying outlier plans or regions when using projective averages.

We characterize the structure and origins of missingness for 159 cross-sectional return predictors and study missing value handling for portfolios constructed using machine learning. Simply imputing with cross-sectional means performs well compared to rigorous expectation-maximization methods. This stems from three facts about predictor data: (1) missingness occurs in large blocks organized by time, (2) cross-sectional correlations are small, and (3) missingness tends to occur in blocks organized by the underlying data source. As a result, observed data provide little information about missing data. Sophisticated imputations introduce estimation noise that can lead to underperformance if machine learning is not carefully applied.

We introduce a calculus of extensional resource terms. These are resource terms \`a la Ehrhard-Regnier, but in infinite $\eta$-long form, while retaining a finite syntax and dynamics: in particular, we prove strong confluence and normalization. Then we define an extensional version of Taylor expansion, mapping ordinary $\lambda$-terms to sets (or infinite linear combinations) of extensional resource terms: just like for ordinary Taylor expansion, the dynamics of our resource calculus allows to simulate the $\beta$-reduction of $\lambda$-terms; the extensional nature of expansion shows in that we are also able to simulate $\eta$-reduction. In a sense, extensional resource terms form a language of (non-necessarily normal) finite approximants of Nakajima trees, much like ordinary resource terms are approximants of B\"ohm-trees. Indeed, we show that the equivalence induced on $\lambda$-terms by the normalization of extensional Taylor-expansion is nothing but $H^*$, the greatest consistent sensible $\lambda$-theory. Taylor expansion has profoundly renewed the approximation theory of the $\lambda$-calculus by providing a quantitative alternative to order-based approximation techniques, such as Scott continuity and B\"ohm trees. Extensional Taylor expansion enjoys similar advantages: e.g., to exhibit models of $H^*$, it is now sufficient to provide a model of the extensional resource calculus. We apply this strategy to give a new, elementary proof of a result by Manzonetto: $H^*$ is the $\lambda$-theory induced by a well-chosen reflexive object in the relational model of the $\lambda$-calculus.

We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving a number of regression problems that is exponential in the number of features, so a Monte Carlo-type approximation is typically used. We focus on the special case of least-squares regression models, where several tricks can be used to compute and evaluate regression models efficiently. These tricks give a substantial speed up, allowing many more Monte Carlo samples to be evaluated, achieving better accuracy. We refer to our method as least-squares Shapley performance attribution (LS-SPA), and describe our open-source implementation.

Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.