Related papers: Formal Primal-Dual Algorithm Analysis
Although we have seen a proliferation of algorithms for recommending visualizations, these algorithms are rarely compared with one another, making it difficult to ascertain which algorithm is best for a given visual analysis scenario.…
The analytic deep prior (ADP) approach was recently introduced for the theoretical analysis of deep image prior (DIP) methods with special network architectures. In this paper, we prove that ADP is in fact equivalent to classical…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Display Ads and the generalized assignment problem are two well-studied online packing problems with important applications in ad allocation and other areas. In both problems, ad impressions arrive online and have to be allocated…
We adapt the Deutsch-Josza algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is…
Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study…
Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes.…
We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention and the main focus is to figure out how large the right-hand…
Increasingly, scholars seek to integrate legal and technological insights to combat bias in AI systems. In recent years, many different definitions for ensuring non-discrimination in algorithmic decision systems have been put forward. In…
Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic languages. Finally, we present a formalized definition of…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…
"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…
We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are…