Few-shot learning (FSL) is a central problem in meta-learning, where learners must efficiently learn from few labeled examples. Within FSL, feature pre-training has recently become an increasingly popular strategy to significantly improve generalization performance. However, the contribution of pre-training is often overlooked and understudied, with limited theoretical understanding of its impact on meta-learning performance. Further, pre-training requires a consistent set of global labels shared across training tasks, which may be unavailable in practice. In this work, we address the above issues by first showing the connection between pre-training and meta-learning. We discuss why pre-training yields more robust meta-representation and connect the theoretical analysis to existing works and empirical results. Secondly, we introduce Meta Label Learning (MeLa), a novel meta-learning algorithm that learns task relations by inferring global labels across tasks. This allows us to exploit pre-training for FSL even when global labels are unavailable or ill-defined. Lastly, we introduce an augmented pre-training procedure that further improves the learned meta-representation. Empirically, MeLa outperforms existing methods across a diverse range of benchmarks, in particular under a more challenging setting where the number of training tasks is limited and labels are task-specific. We also provide extensive ablation study to highlight its key properties.

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d. settings, the latter in terms of mixing coefficients. Our results suggest RRR might be beneficial over other widely used estimators as confirmed in numerical experiments both for forecasting and mode decomposition.

在概率空间或分销回归方面的学习功能的问题正在对机器学习社区产生重大兴趣。此问题背后的一个关键挑战是确定捕获基础功能映射的所有相关属性的合适表示形式。内核平均嵌入式提供了一种原则性的分布回归方法，该方法在概率水平上提高了内核诱导的输入域的相似性。该策略有效地解决了问题的两阶段抽样性质，使人们能够得出具有强大统计保证的估计器，例如普遍的一致性和过度的风险界限。但是，内核平均值嵌入在最大平均差异（MMD）上隐含地铰接，这是概率的度量，可能无法捕获分布之间的关键几何关系。相反，最佳运输（OT）指标可能更具吸引力。在这项工作中，我们提出了一个基于OT的分布回归估计器。我们建立在切成薄片的Wasserstein距离上，以获得基于OT的表示。我们基于这种表示，我们研究了内核脊回归估计量的理论特性，我们证明了普遍的一致性和过多的风险界限。初步实验通过显示提出方法的有效性并将其与基于MMD的估计器进行比较，以补充我们的理论发现。

找到模型概率密度的好方法是概率推断的关键。理想的模型应该能够简单地近似于概率，同时也与两个主要操作兼容：两个模型（产品规则）的乘法和相对于随机变量的子集（SUM规则）的边缘化。在这项工作中，我们表明最近提出的非负函数的正半明确（PSD）模型特别适用于此。特别是，我们表征了PSD模型的近似和泛化能力，显示它们享有强烈的理论保证。此外，我们表明我们可以通过矩阵操作以封闭形式的封闭形式有效地执行和产品规则，享受混合模型的相同多功能性。我们的结果为PSD模型应用于密度估计，决策理论和推理的方式开辟了途径。

Computational units in artificial neural networks follow a simplified model of biological neurons. In the biological model, the output signal of a neuron runs down the axon, splits following the many branches at its end, and passes identically to all the downward neurons of the network. Each of the downward neurons will use their copy of this signal as one of many inputs dendrites, integrate them all and fire an output, if above some threshold. In the artificial neural network, this translates to the fact that the nonlinear filtering of the signal is performed in the upward neuron, meaning that in practice the same activation is shared between all the downward neurons that use that signal as their input. Dendrites thus play a passive role. We propose a slightly more complex model for the biological neuron, where dendrites play an active role: the activation in the output of the upward neuron becomes optional, and instead the signals going through each dendrite undergo independent nonlinear filterings, before the linear combination. We implement this new model into a ReLU computational unit and discuss its biological plausibility. We compare this new computational unit with the standard one and describe it from a geometrical point of view. We provide a Keras implementation of this unit into fully connected and convolutional layers and estimate their FLOPs and weights change. We then use these layers in ResNet architectures on CIFAR-10, CIFAR-100, Imagenette, and Imagewoof, obtaining performance improvements over standard ResNets up to 1.73%. Finally, we prove a universal representation theorem for continuous functions on compact sets and show that this new unit has more representational power than its standard counterpart.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

The visual dimension of cities has been a fundamental subject in urban studies, since the pioneering work of scholars such as Sitte, Lynch, Arnheim, and Jacobs. Several decades later, big data and artificial intelligence (AI) are revolutionizing how people move, sense, and interact with cities. This paper reviews the literature on the appearance and function of cities to illustrate how visual information has been used to understand them. A conceptual framework, Urban Visual Intelligence, is introduced to systematically elaborate on how new image data sources and AI techniques are reshaping the way researchers perceive and measure cities, enabling the study of the physical environment and its interactions with socioeconomic environments at various scales. The paper argues that these new approaches enable researchers to revisit the classic urban theories and themes, and potentially help cities create environments that are more in line with human behaviors and aspirations in the digital age.

General nonlinear sieve learnings are classes of nonlinear sieves that can approximate nonlinear functions of high dimensional variables much more flexibly than various linear sieves (or series). This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectation functionals of time series data, where the functionals of interest are based on some nonparametric function that satisfy conditional moment restrictions and are learned using multilayer neural networks. While the asymptotic normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is asymptotically Chi-square distributed, regardless whether the expectation functional is regular (root-$n$ estimable) or not. This holds when the data are weakly dependent beta-mixing condition. We apply our method to the off-policy evaluation in reinforcement learning, by formulating the Bellman equation into the conditional moment restriction framework, so that we can make inference about the state-specific value functional using the proposed GN-QLR method with time series data. In addition, estimating the averaged partial means and averaged partial derivatives of nonparametric instrumental variables and quantile IV models are also presented as leading examples. Finally, a Monte Carlo study shows the finite sample performance of the procedure

As various city agencies and mobility operators navigate toward innovative mobility solutions, there is a need for strategic flexibility in well-timed investment decisions in the design and timing of mobility service regions, i.e. cast as "real options" (RO). This problem becomes increasingly challenging with multiple interacting RO in such investments. We propose a scalable machine learning based RO framework for multi-period sequential service region design & timing problem for mobility-on-demand services, framed as a Markov decision process with non-stationary stochastic variables. A value function approximation policy from literature uses multi-option least squares Monte Carlo simulation to get a policy value for a set of interdependent investment decisions as deferral options (CR policy). The goal is to determine the optimal selection and timing of a set of zones to include in a service region. However, prior work required explicit enumeration of all possible sequences of investments. To address the combinatorial complexity of such enumeration, we propose a new variant "deep" RO policy using an efficient recurrent neural network (RNN) based ML method (CR-RNN policy) to sample sequences to forego the need for enumeration, making network design & timing policy tractable for large scale implementation. Experiments on multiple service region scenarios in New York City (NYC) shows the proposed policy substantially reduces the overall computational cost (time reduction for RO evaluation of > 90% of total investment sequences is achieved), with zero to near-zero gap compared to the benchmark. A case study of sequential service region design for expansion of MoD services in Brooklyn, NYC show that using the CR-RNN policy to determine optimal RO investment strategy yields a similar performance (0.5% within CR policy value) with significantly reduced computation time (about 5.4 times faster).

The problem of detecting the Out-of-Distribution (OoD) inputs is of paramount importance for Deep Neural Networks. It has been previously shown that even Deep Generative Models that allow estimating the density of the inputs may not be reliable and often tend to make over-confident predictions for OoDs, assigning to them a higher density than to the in-distribution data. This over-confidence in a single model can be potentially mitigated with Bayesian inference over the model parameters that take into account epistemic uncertainty. This paper investigates three approaches to Bayesian inference: stochastic gradient Markov chain Monte Carlo, Bayes by Backpropagation, and Stochastic Weight Averaging-Gaussian. The inference is implemented over the weights of the deep neural networks that parameterize the likelihood of the Variational Autoencoder. We empirically evaluate the approaches against several benchmarks that are often used for OoD detection: estimation of the marginal likelihood utilizing sampled model ensemble, typicality test, disagreement score, and Watanabe-Akaike Information Criterion. Finally, we introduce two simple scores that demonstrate the state-of-the-art performance.