We address the problem of integrating data from multiple observational and interventional studies to eventually compute counterfactuals in structural causal models. We derive a likelihood characterisation for the overall data that leads us to extend a previous EM-based algorithm from the case of a single study to that of multiple ones. The new algorithm learns to approximate the (unidentifiability) region of model parameters from such mixed data sources. On this basis, it delivers interval approximations to counterfactual results, which collapse to points in the identifiable case. The algorithm is very general, it works on semi-Markovian models with discrete variables and can compute any counterfactual. Moreover, it automatically determines if a problem is feasible (the parameter region being nonempty), which is a necessary step not to yield incorrect results. Systematic numerical experiments show the effectiveness and accuracy of the algorithm, while hinting at the benefits of integrating heterogeneous data to get informative bounds in case of unidentifiability.

自动评估学习者能力是智能辅导系统中的一项基本任务。评估专栏通常有效地描述了相关能力和能力水平。本文介绍了一种直接从评估标题定义某些（部分）能力级别的评估标题中得出学习者模型的方法。该模型基于贝叶斯网络，并以不确定性（通常称为嘈杂的门）利用逻辑门来减少模型的参数数量，因此，以简化专家的启发并允许对智能辅导系统的实时推断。我们说明了如何应用该方法来自动对用于测试计算思维技能的活动的人类评估。从评估主题开始的模型的简单启发打开了快速自动化几个任务的自动化的可能性，从而使它们在自适应评估工具和智能辅导系统的背景下更容易利用。

我们提出了一种对任何概率基础预测进行核对的原则方法。我们展示了如何通过通过贝叶斯规则合并底部预测和上层时间序列中包含的信息来获得概率对帐。我们在玩具层次结构上说明了我们的方法，展示了我们的框架如何允许对任何基本预测的概率对帐。我们对计数时间序列的时间层次结构进行对帐进行实验，与基于高斯或截短的高斯分布相比，获得了重大改进。

我们介绍了AdapQuest，这是一种用Java编写的软件工具，用于基于贝叶斯网络的自适应问卷发展。适应性在此作为问题序列的动态选择，基于测试接受者技能水平的不断发展的模型。贝叶斯网络提供灵活且高度可解释的框架来描述此类测试过程，尤其是在应对多种技能时。AdapQuest嵌入了专用的阐述策略，以简化问卷参数的引发。该工具用于诊断精神障碍的工具也与一些实施细节一起讨论。

结构因果模型是珍珠因果理论的基本建模单元;原则上，他们允许我们解决反事实，这些反应性是因果关系阶梯的顶部梯级。但它们通常包含将其应用程序应用于特殊设置的潜在变量。这似乎是本文证明的事实的结果，即使在具有聚节形图所表征的模型中，也是NP - 硬的因果推断。为了处理这种硬度，我们介绍了因果EM算法。其主要目标是从关于分类清单变量的数据重建关于潜在变量的不确定性。然后通过贝叶斯网络的标准算法解决反事实推断。结果是近似计算反事实的一般方法，是它们可识别的或不可识别（在这种情况下，我们提供界限）。我们经验展示，以及通过导出可靠的间隔，我们提供的近似在展开的EM运行中得到准确。这些结果终于争辩说，似乎对趋势的想法似乎不受注意到的趋势概念，即不知道结构方程，通常可以计算反事实界。

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.

Fruit is a key crop in worldwide agriculture feeding millions of people. The standard supply chain of fruit products involves quality checks to guarantee freshness, taste, and, most of all, safety. An important factor that determines fruit quality is its stage of ripening. This is usually manually classified by experts in the field, which makes it a labor-intensive and error-prone process. Thus, there is an arising need for automation in the process of fruit ripeness classification. Many automatic methods have been proposed that employ a variety of feature descriptors for the food item to be graded. Machine learning and deep learning techniques dominate the top-performing methods. Furthermore, deep learning can operate on raw data and thus relieve the users from having to compute complex engineered features, which are often crop-specific. In this survey, we review the latest methods proposed in the literature to automatize fruit ripeness classification, highlighting the most common feature descriptors they operate on.

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms.

In contextual linear bandits, the reward function is assumed to be a linear combination of an unknown reward vector and a given embedding of context-arm pairs. In practice, the embedding is often learned at the same time as the reward vector, thus leading to an online representation learning problem. Existing approaches to representation learning in contextual bandits are either very generic (e.g., model-selection techniques or algorithms for learning with arbitrary function classes) or specialized to particular structures (e.g., nested features or representations with certain spectral properties). As a result, the understanding of the cost of representation learning in contextual linear bandit is still limited. In this paper, we take a systematic approach to the problem and provide a comprehensive study through an instance-dependent perspective. We show that representation learning is fundamentally more complex than linear bandits (i.e., learning with a given representation). In particular, learning with a given set of representations is never simpler than learning with the worst realizable representation in the set, while we show cases where it can be arbitrarily harder. We complement this result with an extensive discussion of how it relates to existing literature and we illustrate positive instances where representation learning is as complex as learning with a fixed representation and where sub-logarithmic regret is achievable.