Human perception of the empirical world involves recognizing the diverse appearances, or 'modalities', of underlying objects. Despite the longstanding consideration of this perspective in philosophy and cognitive science, the study of multimodality remains relatively under-explored within the field of machine learning. Nevertheless, current studies of multimodal machine learning are limited to empirical practices, lacking theoretical foundations beyond heuristic arguments. An intriguing finding from the practice of multimodal learning is that a model trained on multiple modalities can outperform a finely-tuned unimodal model, even on unimodal tasks. This paper provides a theoretical framework that explains this phenomenon, by studying generalization properties of multimodal learning algorithms. We demonstrate that multimodal learning allows for a superior generalization bound compared to unimodal learning, up to a factor of $O(\sqrt{n})$, where $n$ represents the sample size. Such advantage occurs when both connection and heterogeneity exist between the modalities.

We investigate theoretically how the features of a two-layer neural network adapt to the structure of the target function through a few large batch gradient descent steps, leading to improvement in the approximation capacity with respect to the initialization. We compare the influence of batch size and that of multiple (but finitely many) steps. For a single gradient step, a batch of size $n = \mathcal{O}(d)$ is both necessary and sufficient to align with the target function, although only a single direction can be learned. In contrast, $n = \mathcal{O}(d^2)$ is essential for neurons to specialize to multiple relevant directions of the target with a single gradient step. Even in this case, we show there might exist ``hard'' directions requiring $n = \mathcal{O}(d^\ell)$ samples to be learned, where $\ell$ is known as the leap index of the target. The picture drastically improves over multiple gradient steps: we show that a batch-size of $n = \mathcal{O}(d)$ is indeed enough to learn multiple target directions satisfying a staircase property, where more and more directions can be learned over time. Finally, we discuss how these directions allows to drastically improve the approximation capacity and generalization error over the initialization, illustrating a separation of scale between the random features/lazy regime, and the feature learning regime. Our technical analysis leverages a combination of techniques related to concentration, projection-based conditioning, and Gaussian equivalence which we believe are of independent interest. By pinning down the conditions necessary for specialization and learning, our results highlight the interaction between batch size and number of iterations, and lead to a hierarchical depiction where learning performance exhibits a stairway to accuracy over time and batch size, shedding new light on how neural networks adapt to features of the data.

Decision makers often aim to learn a treatment assignment policy under a capacity constraint on the number of agents that they can treat. When agents can respond strategically to such policies, competition arises, complicating estimation of the optimal policy. In this paper, we study capacity-constrained treatment assignment in the presence of such interference. We consider a dynamic model where the decision maker allocates treatments at each time step and heterogeneous agents myopically best respond to the previous treatment assignment policy. When the number of agents is large but finite, we show that the threshold for receiving treatment under a given policy converges to the policy's mean-field equilibrium threshold. Based on this result, we develop a consistent estimator for the policy gradient. In simulations and a semi-synthetic experiment with data from the National Education Longitudinal Study of 1988, we demonstrate that this estimator can be used for learning capacity-constrained policies in the presence of strategic behavior.

This paper studies the problem of CPRP, concept prerequisite relation prediction, which is a fundamental task in using AI for education. CPRP is usually formulated into a link-prediction task on a relationship graph of concepts and solved by training the graph neural network (GNN) model. However, current directed GNNs fail to manage graph isomorphism which refers to the invariance of non-isomorphic graphs, reducing the expressivity of resulting representations. We present a permutation-equivariant directed GNN model by introducing the Weisfeiler-Lehman test into directed GNN learning. Our method is then used for CPRP and evaluated on three public datasets. The experimental results show that our model delivers better prediction performance than the state-of-the-art methods.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Much research has been devoted to the problem of learning fair representations; however, they do not explicitly the relationship between latent representations. In many real-world applications, there may be causal relationships between latent representations. Furthermore, most fair representation learning methods focus on group-level fairness and are based on correlations, ignoring the causal relationships underlying the data. In this work, we theoretically demonstrate that using the structured representations enable downstream predictive models to achieve counterfactual fairness, and then we propose the Counterfactual Fairness Variational AutoEncoder (CF-VAE) to obtain structured representations with respect to domain knowledge. The experimental results show that the proposed method achieves better fairness and accuracy performance than the benchmark fairness methods.

Multi-agent reinforcement learning (MARL) research is inherently computationally expensive and it is often difficult to obtain a sufficient number of experiment samples to test hypotheses and make robust statistical claims. Furthermore, MARL algorithms are typically complex in their design and can be tricky to implement correctly. These aspects of MARL present a difficult challenge when it comes to creating useful software for advanced research. Our criteria for such software is that it should be simple enough to use to implement new ideas quickly, while at the same time be scalable and fast enough to test those ideas in a reasonable amount of time. In this preliminary technical report, we introduce Mava, a research library for MARL written purely in JAX, that aims to fulfill these criteria. We discuss the design and core features of Mava, and demonstrate its use and performance across a variety of environments. In particular, we show Mava's substantial speed advantage, with improvements of 10-100x compared to other popular MARL frameworks, while maintaining strong performance. This allows for researchers to test ideas in a few minutes instead of several hours. Finally, Mava forms part of an ecosystem of libraries that seamlessly integrate with each other to help facilitate advanced research in MARL. We hope Mava will benefit the community and help drive scientifically sound and statistically robust research in the field. The open-source repository for Mava is available at https://github.com/instadeepai/Mava.

Evaluating the average causal effect (ACE) of a treatment on an outcome often involves overcoming the challenges posed by confounding factors in observational studies. A traditional approach uses the back-door criterion, seeking adjustment sets to block confounding paths between treatment and outcome. However, this method struggles with unmeasured confounders. As an alternative, the front-door criterion offers a solution, even in the presence of unmeasured confounders between treatment and outcome. This method relies on identifying mediators that are not directly affected by these confounders and that completely mediate the treatment's effect. Here, we introduce novel estimation strategies for the front-door criterion based on the targeted minimum loss-based estimation theory. Our estimators work across diverse scenarios, handling binary, continuous, and multivariate mediators. They leverage data-adaptive machine learning algorithms, minimizing assumptions and ensuring key statistical properties like asymptotic linearity, double-robustness, efficiency, and valid estimates within the target parameter space. We establish conditions under which the nuisance functional estimations ensure the root n-consistency of ACE estimators. Our numerical experiments show the favorable finite sample performance of the proposed estimators. We demonstrate the applicability of these estimators to analyze the effect of early stage academic performance on future yearly income using data from the Finnish Social Science Data Archive.

Recent advances in learning techniques have garnered attention for their applicability to a diverse range of real-world sequential decision-making problems. Yet, many practical applications have critical constraints for operation in real environments. Most learning solutions often neglect the risk of failing to meet these constraints, hindering their implementation in real-world contexts. In this paper, we propose a risk-aware decision-making framework for contextual bandit problems, accommodating constraints and continuous action spaces. Our approach employs an actor multi-critic architecture, with each critic characterizing the distribution of performance and constraint metrics. Our framework is designed to cater to various risk levels, effectively balancing constraint satisfaction against performance. To demonstrate the effectiveness of our approach, we first compare it against state-of-the-art baseline methods in a synthetic environment, highlighting the impact of intrinsic environmental noise across different risk configurations. Finally, we evaluate our framework in a real-world use case involving a 5G mobile network where only our approach consistently satisfies the system constraint (a signal processing reliability target) with a small performance toll (8.5% increase in power consumption).

Power efficiency is a critical design objective in modern microprocessor design. To evaluate the impact of architectural-level design decisions, an accurate yet efficient architecture-level power model is desired. However, widely adopted data-independent analytical power models like McPAT and Wattch have been criticized for their unreliable accuracy. While some machine learning (ML) methods have been proposed for architecture-level power modeling, they rely on sufficient known designs for training and perform poorly when the number of available designs is limited, which is typically the case in realistic scenarios. In this work, we derive a general formulation that unifies existing architecture-level power models. Based on the formulation, we propose PANDA, an innovative architecture-level solution that combines the advantages of analytical and ML power models. It achieves unprecedented high accuracy on unknown new designs even when there are very limited designs for training, which is a common challenge in practice. Besides being an excellent power model, it can predict area, performance, and energy accurately. PANDA further supports power prediction for unknown new technology nodes. In our experiments, besides validating the superior performance and the wide range of functionalities of PANDA, we also propose an application scenario, where PANDA proves to identify high-performance design configurations given a power constraint.