Related papers: Improving Point and Interval Estimates of Monotone…
We develop estimation and inference methods for a stylized macroeconomic model with potentially multiple behavioural equilibria, where agents form expectations using a constant-gain learning rule. We first show geometric ergodicity of the…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
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…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance…
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
Regression adjustment, sometimes known as Controlled-experiment Using Pre-Experiment Data (CUPED), is an important technique in internet experimentation. It decreases the variance of effect size estimates, often cutting confidence interval…
We study the problem of conformal prediction in a novel online framework that directly optimizes efficiency. In our problem, we are given a target miscoverage rate $\alpha > 0$, and a time horizon $T$. On each day $t \le T$ an algorithm…
Recent work has shown that data augmentation has the potential to significantly improve the generalization of deep learning models. Recently, automated augmentation strategies have led to state-of-the-art results in image classification and…
We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the…
In machine learning, an agent needs to estimate uncertainty to efficiently explore and adapt and to make effective decisions. A common approach to uncertainty estimation maintains an ensemble of models. In recent years, several approaches…
Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions and to impose additional constraints on them. Monotonicity constraint is one of the most…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects…
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…
Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Multi-agent coordination algorithms with randomized interactions have seen use in a variety of settings in the multi-agent systems literature. In some cases, these algorithms can be random by design, as in a gossip-like algorithm, and in…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…