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We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability…
We consider the secretary problem through the lens of learning-augmented algorithms. As it is known that the best possible expected competitive ratio is $1/e$ in the classic setting without predictions, a natural goal is to design…
Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more…
An important issue in concurrency is interference. This issue manifests itself in both shared-variable and communication-based concurrency --- this paper focusses on the former case where interference is caused by the environment of a…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
In generalized malleable scheduling, jobs can be allocated and processed simultaneously on multiple machines so as to reduce the overall makespan of the schedule. The required processing time for each job is determined by the joint…
Code corpora, as observed in large software systems, are now known to be far more repetitive and predictable than natural language corpora. But why? Does the difference simply arise from the syntactic limitations of programming languages?…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…
Intermediate variables can be used to break complex expressions into more manageable smaller expressions, which may be easier to understand. But it is unclear when and whether this actually helps. We conducted an experiment in which…
When it is ethical and legal to use a sensitive attribute (such as gender or race) in machine learning systems, the question remains how to do so. We show that the naive application of machine learning algorithms using sensitive features…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
Formulating a real-world problem under the Reinforcement Learning framework involves non-trivial design choices, such as selecting a discount factor for the learning objective (discounted cumulative rewards), which articulates the planning…