Home Research Curriculum Vitae

Jonathan Vandenburgh

Below, you can find a list of papers. For papers not available online, please contact me if you would like to see a draft.

Machine Learning and Knowledge: Why Robustness Matters

Available on arXiv: https://arxiv.org/pdf/2310.19819v1.pdf

Trusting machine learning algorithms requires having confidence in their outputs. Confidence is typically interpreted in terms of model reliability, where a model is reliable if it produces a high proportion of correct outputs. However, model reliability does not address concerns about the robustness of machine learning models, such as models relying on the wrong features or variations in performance based on context. I argue that the epistemic dimension of trust can instead be understood through the concept of knowledge, where the trustworthiness of an algorithm depends on whether its users are in the position to know that its outputs are correct. Knowledge requires beliefs to be formed for the right reasons and to be robust to error, so machine learning algorithms can only provide knowledge if they work well across counterfactual scenarios and if they make decisions based on the right features. This, I argue, can explain why we should care about model properties like interpretability, causal shortcut independence, and distribution shift robustness even if such properties are not required for model reliability.

A Causal Safety Criterion for Knowledge

Available in Erkenntnis: https://rdcu.be/c8loC

Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, problems arise for using safety as a condition on knowledge: safety is not necessary for knowledge and cannot always explain the Gettier cases and cases of statistical evidence it is meant to address. In this paper, I argue for a new modal condition designed to capture the non-accidental relationship between facts and evidence required for knowledge: causal safety. I argue that possible errors in belief can be captured by accounting for deviations in causal relationships and that there is a natural way to characterize which causal errors are relevant in an epistemic situation. Using this, I develop a causal analogue to safety, where one’s belief in p is causally safe if it is true in all causally relevant worlds where one believes p. Causal safety, I argue, can better explain the cases safety is meant to address and can avoid the arguments raised against the necessity of safety.

Backtracking Through Interventions: an Exogenous Intervention Model for Counterfactual Semantics

Available in Mind & Language:

Causal models show promise as a foundation for the semantics of counterfactual sentences. However, current approaches face limitations compared to the alternative similarity theory: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This paper addresses these difficulties using exogenous interventions, where causal interventions change the values of exogenous variables rather than structural equations. This model accommodates judgments about backtracking counterfactuals, extends to logically complex counterfactuals, and validates familiar principles of counterfactual logic. This combines the interventionist intuitions of the causal approach with the logical advantages of the similarity approach.

Conditional Learning Through Causal Models

Available in Synthese: https://rdcu.be/b7VNz

Conditional learning, where agents learn a conditional sentence 'If A, then B,' is difficult to incorporate into existing Bayesian models of learning. This is because conditional learning is not uniform: in some cases, learning a conditional requires decreasing the probability of the antecedent, while in other cases, the antecedent probability stays constant or increases. I argue that how one learns a conditional depends on the causal structure relating the antecedent and the consequent, leading to a causal model of conditional learning. This model extends traditional Bayesian learning by incorporating causal models into agents' epistemic states. On this theory, conditional learning proceeds in two steps. First, an agent learns a new causal model with the appropriate relationship between the antecedent and the consequent. Then, the agent narrows down the set of possible worlds to include only those which make the conditional proposition true. This model of learning can incorporate both standard cases of Bayesian learning and the non-uniform learning required to learn conditional information.

Triviality Results, Conditional Probability, and Restrictor Conditionals

Available on PhilPapers: https://philpapers.org/archive/VANTRC-4.pdf

Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor theory can avoid these problematic assumptions. In doing so, I argue that recent extensions of the triviality arguments to restrictor conditionals fail, making assumptions which are only justified on the operator theory.

Learning as Hypothesis Testing: Learning Conditional and Probabilistic Information

Available on PhilPapers: https://philpapers.org/archive/VANLAH-5.pdf

The history of science is often conceptualized through 'paradigm shifts,' where the accumulation of evidence leads to abrupt changes in scientific theories. Experimental evidence suggests that this kind of hypothesis revision occurs in more mundane circumstances, such as when children learn concepts and when adults engage in strategic behavior. In this paper, I argue that the model of hypothesis testing can explain how people learn certain complex, theory-laden propositions such as conditional sentences ('If A, then B') and probabilistic constraints ('The probability that A is p'). Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. The model of hypothesis testing is contrasted with the more conservative learning theory of relative information minimization, which dominates current approaches to learning conditional and probabilistic information.