arXiv research

A coin-flipping game paradox illustrates how conditional probability estimation can distort risk assessment.

We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.

Non-ergodic measures found in horocycle flow on Abelian differentials.

The paper explores properties of functions on Teichmüller space, proving theorems about limits and non-ergodicity.

Non-ergodic geodesic flow on Cantor tree surfaces found.

New rule universally consistent for online learning with non-ergodic data.

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a re…

We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.

The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel results, especially on the convergence rates of the objective function values. The no…

We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its …

This essay discusses the advantages of a probabilistic agent-based approach to questions in theoretical economics, from the nature of economic agents, to the nature of the equilibria supported by their interactions. One idea we propose is that "agents" are meta-individual, hierarchically structured objects, that includ…

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…

Analyzes non-Markovian environments in stochastic approximation.

We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …

Sandpile Economics explains how economies can be prone to large crises from small shocks.

Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…

In the paper, we construct conservative Markov processes corresponding to the martingale solutions to the stochastic heat equation on $\mathbb{R}^+$ or $\mathbb{R}$ with values in a general Riemannian maifold, which is only assumed to be complete and stochastic complete. This work is an extension of the previous paper …

The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.

Strong stability of ergodic iterations proven without ergodic driving sequence.

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the t…

We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functi…

A framework for hypothesis testing on attributed graphs using sampling.

Study on generalization for data-dependent hypothesis sets.

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that prices evolve according to an ergodic process with a mild decaying memory proper…

Improves estimation of financial market models using limited data.

The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.

Hypothesis testing is an important problem with applications in target localization, clinical trials etc. Many active hypothesis testing strategies operate in two phases: an exploration phase and a verification phase. In the exploration phase, selection of experiments is such that a moderate level of confidence on the …

Learnable multiclass hypothesis classes don't always have a sample compression scheme of fixed size.

Paper proposes an algorithm to reduce hypothesis space for faster convergence in high-dimensional settings.

Paper resolves open problems on sample complexity in binary hypothesis testing.

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphi…

New bounds improve generalization in learning scenarios.

Hypothesis identifies useful transformations for self-supervised learning.

Paper tackles hypothesis transfer learning for black-box models.

Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.

Unified Bayesian framework improves clinical trial hypothesis testing.

U-turn chains improve sampling from complex distributions.

Study robust hypothesis testing under Hellinger distance, proving lower bounds and providing tests.

The paper refutes the manifold hypothesis for image data and proposes the union of manifolds hypothesis.

We improve adversarial robustness calibration analysis for broader hypothesis sets.

The Greenberg-Shalom hypothesis connects subgroup properties to lattice structures in Lie groups.

The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing simultaneously the significance of all frequent itemsets of a single dataset entai…

New private algorithm for sequential hypothesis testing with privacy and error rate guarantees.

Paper proposes a robust hypothesis testing method using Sinkhorn distance.

Paper proposes a new framework for hypothesis testing in imaging.

Comparative learning combines realizable and agnostic settings for two hypothesis classes, reducing sample complexity.

Efficient algorithms identify true hypothesis from many options with minimal actions.