Related papers: Loss Bounds and Time Complexity for Speed Priors
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
The existence of a pivot rule for the simplex method that guarantees a strongly polynomial run-time is a longstanding, fundamental open problem in the theory of linear programming. The leading pivot rule in theory is the shadow pivot rule,…
We develop conjectures and theorems expressing the idea that the prime sequence exhibits computational irreducibility in the transition from one prime to its successor. Informally, given a prime pp p, no general algorithm can compute the…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
Solomonoff sequence prediction is a scheme to predict digits of binary strings without knowing the underlying probability distribution. We call a prediction scheme informed when it knows the true probability distribution of the sequence.…
Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the…
We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [V\'egh16]. For the uncapacitated problem formulation, the complexity…
The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this…
Advancements in computational power and methodologies have enabled research on massive datasets. However, tools for analyzing data with directional or periodic characteristics, such as wind directions and customers' arrival time in 24-hour…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We continue the study of counting complexity begun in [Buergisser, Cucker 04] and [Buergisser, Cucker, Lotz 05] by proving upper and lower bounds on the complexity of computing the Hilbert polynomial of a homogeneous ideal. We show that the…
We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor $M$ from the true distribution $mu$ by the algorithmic complexity of $mu$. Here…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
This paper is concerned with the propagating speeds of transition fronts in $R^N$ for spatially periodic bistable reaction-diffusion equations. The notion of transition fronts generalizes the standard notions of traveling fronts. Under the…
We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs…
Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors.…
We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a…