Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the discretized data, and there are no semantics in the modeling process that relate the observed data to the underlying functional forms. We generalize diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces. A significant benefit of our function space point of view is that it allows us to explicitly specify the space of functions we are working in, leading us to develop methods for diffusion generative modeling in Sobolev spaces. Our approach allows us to perform both unconditional and conditional generation of function-valued data. We demonstrate our methods on several synthetic and real-world benchmarks.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

The deployment of machine learning classifiers in high-stakes domains requires well-calibrated confidence scores for model predictions. In this paper we introduce the notion of variable-based calibration to characterize calibration properties of a model with respect to a variable of interest, generalizing traditional score-based calibration and metrics such as expected calibration error (ECE). In particular, we find that models with near-perfect ECE can exhibit significant variable-based calibration error as a function of features of the data. We demonstrate this phenomenon both theoretically and in practice on multiple well-known datasets, and show that it can persist after the application of existing recalibration methods. To mitigate this issue, we propose strategies for detection, visualization, and quantification of variable-based calibration error. We then examine the limitations of current score-based recalibration methods and explore potential modifications. Finally, we discuss the implications of these findings, emphasizing that an understanding of calibration beyond simple aggregate measures is crucial for endeavors such as fairness and model interpretability.

尽管算法公平最近取得了进步，但通过广义线性模型（GLM）实现公平性的方法论，尽管GLM在实践中广泛使用，但尚待探索。在本文中，我们基于预期的结果或对数类似物的均衡介绍了两个公平标准。我们证明，对于GLMS，这两个标准都可以通过基于GLM的线性组件的凸惩罚项来实现，从而允许有效优化。我们还得出了由此产生的公平GLM估计器的理论特性。为了从经验上证明所提出的公平GLM的功效，我们将其与其他众所周知的公平预测方法进行了比较，以用于二进制分类和回归的广泛基准数据集。此外，我们证明了公平的GLM可以为二进制和连续结果以外的一系列响应变量产生公平的预测。

在分布式学习中，中央服务器根据持有本地数据样本的节点提供的更新来训练模型。在一个或多个发送不正确信息（拜占庭对手）的恶意服务器的情况下，用于模型训练的标准算法（例如随机梯度下降（SGD））无法收敛。在本文中，我们提出了Blanchard等人最初提出的通用拜占庭弹性SGD方法的简化收敛理论。[Neurips 2017]。与现有分析相比，我们在（可能是非convex）目标函数（可能是非凸）的标准假设和随机梯度上的灵活假设上表明了收敛到固定点的固定点。

由于它存在的挑战以及甚至进行预测准确性或预测的潜在奖励，财务预测是机器学习研究的一个重要而活跃的机器学习研究领域。传统上，财务预测严重依赖于结构化财务报表的定量指标和指标。盈利会议呼叫数据（包括文本和音频）是使用深度盈利和相关方法的各种预测任务的重要非结构化数据的重要来源。但是，当前基于深度学习的方法在他们处理数字数据的方式有限;数字通常被视为普通文本令牌，而不利用其底层数字结构。本文介绍了一个以数字为导向的分层变压器模型，以预测库存退货，以及使用多模态对齐收益的财务风险通过利用不同类别的数字（货币，时间，百分比等）及其幅度来调用数据。我们使用现实世界公共可公共数据集介绍了对几个最先进的基线的NumHTML的全面评估结果。结果表明，NumHTML在各种评估指标中显着优于当前最先进的指标，并且它有可能在实际交易环境中提供重大的财务收益。