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COMBINATORIAL ALGORITHMS FOR GRAPH DISCOVERY AND EXPERIMENTAL DESIGN
In this thesis, we study the design and analysis of algorithms for discovering the structure and properties of an unknown graph, with applications in two different domains: causal inference and sublinear graph algorithms. In both these domains, graph discovery is possible using restricted forms of experiments, and our objective is to design low-cost experiments.
First, we describe efficient experimental approaches to the causal discovery problem, which in its simplest form, asks us to identify the causal relations (edges of the unknown graph) between variables (vertices of the unknown graph) of a given system. For causal discovery, we study algorithms for the problem of learning the causal relationships between a set of observed variables in the presence of hidden or unobserved variables while minimizing a suitable cost of interventions on the observed variables. An intervention on a set of variables helps learn the presence of causal relations adjacent to them. Under various cost models for interventions, we design combinatorial algorithms for causal discovery by identifying new connections between discrete optimization, graph property testing, and efficient intervention design.
Next, we investigate query-efficient experimental approaches for estimating various graph properties, such as the number of edges and graph connectivity. The access to the graph, or equivalently performing an experiment, is via a Bipartite Independent Set (BIS) oracle. The BIS oracle is related to the interventional access model used in our work for causal graph discovery, with other applications in group testing and fine-grained complexity. In this setting, we develop non-adaptive algorithms that lead to efficient implementations in highly parallelized and low-memory streaming settings
Nonparametric Identifiability of Causal Representations from Unknown Interventions
We study causal representation learning, the task of inferring latent causal
variables and their causal relations from high-dimensional functions
("mixtures") of the variables. Prior work relies on weak supervision, in the
form of counterfactual pre- and post-intervention views or temporal structure;
places restrictive assumptions, such as linearity, on the mixing function or
latent causal model; or requires partial knowledge of the generative process,
such as the causal graph or the intervention targets. We instead consider the
general setting in which both the causal model and the mixing function are
nonparametric. The learning signal takes the form of multiple datasets, or
environments, arising from unknown interventions in the underlying causal
model. Our goal is to identify both the ground truth latents and their causal
graph up to a set of ambiguities which we show to be irresolvable from
interventional data. We study the fundamental setting of two causal variables
and prove that the observational distribution and one perfect intervention per
node suffice for identifiability, subject to a genericity condition. This
condition rules out spurious solutions that involve fine-tuning of the
intervened and observational distributions, mirroring similar conditions for
nonlinear cause-effect inference. For an arbitrary number of variables, we show
that two distinct paired perfect interventions per node guarantee
identifiability. Further, we demonstrate that the strengths of causal
influences among the latent variables are preserved by all equivalent
solutions, rendering the inferred representation appropriate for drawing causal
conclusions from new data. Our study provides the first identifiability results
for the general nonparametric setting with unknown interventions, and
elucidates what is possible and impossible for causal representation learning
without more direct supervision
Combining experiments to discover linear cyclic models with latent variables
Volume: Vol 9 : AISTATS 2010 Host publication title: Proceedings of the 13th International Conference on Artificial Intelligence and StatisticsPeer reviewe
Learning Linear Causal Representations from Interventions under General Nonlinear Mixing
We study the problem of learning causal representations from unknown, latent
interventions in a general setting, where the latent distribution is Gaussian
but the mixing function is completely general. We prove strong identifiability
results given unknown single-node interventions, i.e., without having access to
the intervention targets. This generalizes prior works which have focused on
weaker classes, such as linear maps or paired counterfactual data. This is also
the first instance of causal identifiability from non-paired interventions for
deep neural network embeddings. Our proof relies on carefully uncovering the
high-dimensional geometric structure present in the data distribution after a
non-linear density transformation, which we capture by analyzing quadratic
forms of precision matrices of the latent distributions. Finally, we propose a
contrastive algorithm to identify the latent variables in practice and evaluate
its performance on various tasks.Comment: 38 page
Learning nonparametric latent causal graphs with unknown interventions
We establish conditions under which latent causal graphs are
nonparametrically identifiable and can be reconstructed from unknown
interventions in the latent space. Our primary focus is the identification of
the latent structure in measurement models without parametric assumptions such
as linearity or Gaussianity. Moreover, we do not assume the number of hidden
variables is known, and we show that at most one unknown intervention per
hidden variable is needed. This extends a recent line of work on learning
causal representations from observations and interventions. The proofs are
constructive and introduce two new graphical concepts -- imaginary subsets and
isolated edges -- that may be useful in their own right. As a matter of
independent interest, the proofs also involve a novel characterization of the
limits of edge orientations within the equivalence class of DAGs induced by
unknown interventions. These are the first results to characterize the
conditions under which causal representations are identifiable without making
any parametric assumptions in a general setting with unknown interventions and
without faithfulness.Comment: To appear at NeurIPS 202
Advancing probabilistic and causal deep learning in medical image analysis
The power and flexibility of deep learning have made it an indispensable tool for tackling modern machine learning problems.
However, this flexibility comes at the cost of robustness and interpretability, which can lead to undesirable or even harmful outcomes. Deep learning models often fail to generalise to real-world conditions and produce unforeseen errors that hinder wide adoption in safety-critical critical domains such as healthcare. This thesis presents multiple works that address the reliability problems of deep learning in safety-critical domains by being aware of its vulnerabilities and incorporating more domain knowledge when designing and evaluating our algorithms.
We start by showing how close collaboration with domain experts is necessary to achieve good results in a real-world clinical task - the multiclass semantic segmentation of traumatic brain injuries (TBI) lesions in head CT.
We continue by proposing an algorithm that models spatially coherent aleatoric uncertainty in segmentation tasks by considering the dependencies between pixels. The lack of proper uncertainty quantification is a robustness issue which is ubiquitous in deep learning. Tackling this issue is of the utmost importance if we want to deploy these systems in the real world.
Lastly, we present a general framework for evaluating image counterfactual inference models in the absence of ground-truth counterfactuals. Counterfactuals are extremely useful to reason about models and data and to probe models for explanations or mistakes. As a result, their evaluation is critical for improving the interpretability of deep learning models.Open Acces
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