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Additive Noise Models (ANM) encode a popular functional assumption that enables learning causal structure from observational data. Due to a lack of real-world data meeting the assumptions, synthetic ANM data are often used to evaluate causal discovery algorithms. Reisach et al. (2021) show that, for common simulation parameters, a variable ordering by increasing variance is closely aligned with a causal order and introduce var-sortability to quantify the alignment. Here, we show that not only variance, but also the fraction of a variable's variance explained by all others, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. Simple baseline algorithms can use $R^2$-sortability to match the performance of established methods. Since $R^2$-sortability is invariant under data rescaling, these algorithms perform equally well on standardized or rescaled data, addressing a key limitation of algorithms exploiting var-sortability. We characterize and empirically assess $R^2$-sortability for different simulation parameters. We show that all simulation parameters can affect $R^2$-sortability and must be chosen deliberately to control the difficulty of the causal discovery task and the real-world plausibility of the simulated data. We provide an implementation of the sortability measures and sortability-based algorithms in our library CausalDisco (//github.com/CausalDisco/CausalDisco).

The Age of Incorrect Information (AoII) is a recently proposed metric for real-time remote monitoring systems. In particular, AoII measures the time the information at the monitor is incorrect, weighted by the magnitude of this incorrectness, thereby combining the notions of freshness and distortion. This paper addresses the definition of an AoII-optimal transmission policy in a discrete-time communication scheme with a resource constraint and a hybrid automatic repeat request (HARQ) protocol. Considering an $N$-ary symmetric Markov source, the problem is formulated as an infinite-horizon average-cost constrained Markov decision process (CMDP). The source model is characterized by the cardinality of the state space and the probability of staying at the same state. Interestingly, it is proved that under some conditions, the optimal transmission policy is to never transmit. This reveals that there exists a region of the source dynamics where communication is inadequate in reducing the AoII. Elsewhere, there exists an optimal transmission policy, which is a randomized mixture of two discrete threshold-based policies that randomize at one state. The optimal threshold and the randomization component are derived analytically. Numerical results illustrate the impact of source dynamics, channel conditions, and the resource constraint on the average AoII.

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

Data-driven offline model-based optimization (MBO) is an established practical approach to black-box computational design problems for which the true objective function is unknown and expensive to query. However, the standard approach which optimizes designs against a learned proxy model of the ground truth objective can suffer from distributional shift. Specifically, in high-dimensional design spaces where valid designs lie on a narrow manifold, the standard approach is susceptible to producing out-of-distribution, invalid designs that "fool" the learned proxy model into outputting a high value. Using an ensemble rather than a single model as the learned proxy can help mitigate distribution shift, but naive formulations for combining gradient information from the ensemble, such as minimum or mean gradient, are still suboptimal and often hampered by non-convergent behavior. In this work, we explore alternate approaches for combining gradient information from the ensemble that are robust to distribution shift without compromising optimality of the produced designs. More specifically, we explore two functions, formulated as convex optimization problems, for combining gradient information: multiple gradient descent algorithm (MGDA) and conflict-averse gradient descent (CAGrad). We evaluate these algorithms on a diverse set of five computational design tasks. We compare performance of ensemble MBO with MGDA and ensemble MBO with CAGrad with three naive baseline algorithms: (a) standard single-model MBO, (b) ensemble MBO with mean gradient, and (c) ensemble MBO with minimum gradient. Our results suggest that MGDA and CAGrad strike a desirable balance between conservatism and optimality and can help robustify data-driven offline MBO without compromising optimality of designs.

Multiple systems estimation is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. A typical modelling approach is to fit a Poisson loglinear model to the numbers of cases observed in each possible combination of the lists. It is necessary to decide which interaction parameters to include in the model, and information criterion approaches are often used for model selection. Difficulties in the context of multiple systems estimation may arise due to sparse or nil counts based on the intersection of lists, and care must be taken when information criterion approaches are used for model selection due to issues relating to the existence of estimates and identifiability of the model. Confidence intervals are often reported conditional on the model selected, providing an over-optimistic impression of the accuracy of the estimation. A bootstrap approach is a natural way to account for the model selection procedure. However, because the model selection step has to be carried out for every bootstrap replication, there may be a high or even prohibitive computational burden. We explore the merit of modifying the model selection procedure in the bootstrap to look only among a subset of models, chosen on the basis of their information criterion score on the original data. This provides large computational gains with little apparent effect on inference. Another model selection approach considered and investigated is a downhill search approach among models, possibly with multiple starting points.

We present a novel technique to estimate the 6D pose of objects from single images where the 3D geometry of the object is only given approximately and not as a precise 3D model. To achieve this, we employ a dense 2D-to-3D correspondence predictor that regresses 3D model coordinates for every pixel. In addition to the 3D coordinates, our model also estimates the pixel-wise coordinate error to discard correspondences that are likely wrong. This allows us to generate multiple 6D pose hypotheses of the object, which we then refine iteratively using a highly efficient region-based approach. We also introduce a novel pixel-wise posterior formulation by which we can estimate the probability for each hypothesis and select the most likely one. As we show in experiments, our approach is capable of dealing with extreme visual conditions including overexposure, high contrast, or low signal-to-noise ratio. This makes it a powerful technique for the particularly challenging task of estimating the pose of tumbling satellites for in-orbit robotic applications. Our method achieves state-of-the-art performance on the SPEED+ dataset and has won the SPEC2021 post-mortem competition.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.