Related papers: Truth Table Minimization of Computational Models
We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Conceptual modeling (CM) applies abstraction to reduce the complexity of a system under study (e.g., an excerpt of reality). As a result of the conceptual modeling process a human interpretable, formalized representation (i.e., a conceptual…
In Direct Sum problems [KRW], one tries to show that for a given computational model, the complexity of computing a collection of finite functions on independent inputs is approximately the sum of their individual complexities. In this…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
We present connections between the recent literature on multigroup fairness for prediction algorithms and classical results in computational complexity. Multiaccurate predictors are correct in expectation on each member of an arbitrary…
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
A major concern of Machine Learning (ML) models is their opacity. They are deployed in an increasing number of applications where they often operate as black boxes that do not provide explanations for their predictions. Among others, the…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Machine learning models in safety-critical settings like healthcare are often blackboxes: they contain a large number of parameters which are not transparent to users. Post-hoc explainability methods where a simple, human-interpretable…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Selecting a subset of the $k$ "best" items from a dataset of $n$ items, based on a scoring function, is a key task in decision-making. Given the rise of automated decision-making software, it is important that the outcome of this process,…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…
In this paper, we assess the complexity results of formalisms that describe the feature theories used in computational linguistics. We show that from these complexity results no immediate conclusions can be drawn about the complexity of the…
Robust model fitting plays a vital role in computer vision, and research into algorithms for robust fitting continues to be active. Arguably the most popular paradigm for robust fitting in computer vision is consensus maximisation, which…
Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…