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Selection statements -- if-then-else, switch and try-catch -- are commonly used in modern imperative programming languages. We propose another selection statement called a {\it choice existentially quantified statement}. This statement…
Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time…
A lens is a single program that specifies two data transformations at once: one transformation converts data from source format to target format and a second transformation inverts the process. Over the past decade, researchers have…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…
We propose an amortized analysis that approximates the resource usage of a Haskell expression. Using the plugin API of GHC, we convert the Haskell code into a simplified representation called GHC Core. We then apply a type-based system…
Language models and software tools are essential to support the continuing vitality of lesser-used languages; however, currently popular neural models require considerable data for training, which normally is not available for such…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Our goal is to build classification models using a combination of free-text and structured data. To do this, we represent structured data by text sentences, DataWords, so that similar data items are mapped into the same sentence. This…
Missing values are unavoidable in many applications of machine learning and present challenges both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as…
As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as…
This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special…
Numerical applications and, more recently, machine learning applications rely on high-dimensional data that is typically organized into multi-dimensional tensors. Many existing frameworks, libraries, and domain-specific languages support…
We introduce a new programming language for expressing reversibility, Energy-Efficient Language (Eel), geared toward algorithm design and implementation. Eel is the first language to take advantage of a partially reversible computation…
Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of "good models", known as Rashomon set. This approach is generically…
There is a widespread need for statistical methods that can analyze high-dimensional datasets with- out imposing restrictive or opaque modeling assumptions. This paper describes a domain-general data analysis method called CrossCat.…
This paper provides a statistical analysis of three common methods of regression for Poisson data in the presence of Poisson background, namely the joint fit with two parametric models for the source and the background, the use of a…