Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSequential Adaptive Design for Jump Regression Estimation
326
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. The first example we undertook was for the purpose of accelerating imaging speed in a high resolution material imaging; the second was use of sequential design for the purpose of mapping a chemical phase diagram. In both examples, the underlying regression functions have discontinuities, so many of the existing design optimization approaches cannot be applied because they mostly assume a continuous regression function. Although some existing adaptive design strategies developed from treed regression models can handle the discontinuities, the Bayesian approaches come with computationally expensive Markov Chain Monte Carlo techniques for posterior inferences and subsequent design point selections, which is not appropriate for the first motivating example that requires computation at least faster than the original imaging speed. In addition, the treed models are based on the domain partitioning that are inefficient when the discontinuities occurs over complex sub-domain boundaries. We propose a simple and effective adaptive design strategy for a regression analysis with discontinuities: some statistical properties with a fixed design will be presented first, and then these properties will be used to propose a new criterion of selecting the design points for the regression analysis. Sequential design with the new criterion will be presented with comprehensive simulated examples, and its application to the two motivating examples will be presented.
rate research
Read More
We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.
The goal of many scientific experiments including A/B testing is to estimate the average treatment effect (ATE), which is defined as the difference between the expected outcomes of two or more treatments. In this paper, we consider a situation where an experimenter can assign a treatment to research subjects sequentially. In adaptive experimental design, the experimenter is allowed to change the probability of assigning a treatment using past observations for estimating the ATE efficiently. However, with this approach, it is difficult to apply a standard statistical method to construct an estimator because the observations are not independent and identically distributed. We thus propose an algorithm for efficient experiments with estimators constructed from dependent samples. We also introduce a sequential testing framework using the proposed estimator. To justify our proposed approach, we provide finite and infinite sample analyses. Finally, we experimentally show that the proposed algorithm exhibits preferable performance.
We advocate for a practical Maximum Likelihood Estimation (MLE) approach for regression and forecasting, as an alternative to the typical approach of Empirical Risk Minimization (ERM) for a specific target metric. This approach is better suited to capture inductive biases such as prior domain knowledge in datasets, and can output post-hoc estimators at inference time that can optimize different types of target metrics. We present theoretical results to demonstrate that our approach is always competitive with any estimator for the target metric under some general conditions, and in many practical settings (such as Poisson Regression) can actually be much superior to ERM. We demonstrate empirically that our method instantiated with a well-designed general purpose mixture likelihood family can obtain superior performance over ERM for a variety of tasks across time-series forecasting and regression datasets with different data distributions.
In this paper we introduce the transductive linear bandit problem: given a set of measurement vectors $mathcal{X}subset mathbb{R}^d$, a set of items $mathcal{Z}subset mathbb{R}^d$, a fixed confidence $delta$, and an unknown vector $theta^{ast}in mathbb{R}^d$, the goal is to infer $text{argmax}_{zin mathcal{Z}} z^toptheta^ast$ with probability $1-delta$ by making as few sequentially chosen noisy measurements of the form $x^toptheta^{ast}$ as possible. When $mathcal{X}=mathcal{Z}$, this setting generalizes linear bandits, and when $mathcal{X}$ is the standard basis vectors and $mathcal{Z}subset {0,1}^d$, combinatorial bandits. Such a transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages $mathcal{X}$ a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages $mathcal{Z}$ that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books $mathcal{X}$ a user is queried about may be restricted to well known best-sellers even though the goal might be to recommend more esoteric titles $mathcal{Z}$. In this paper, we provide instance-dependent lower bounds for the transductive setting, an algorithm that matches these up to logarithmic factors, and an evaluation. In particular, we provide the first non-asymptotic algorithm for linear bandits that nearly achieves the information theoretic lower bound.
Mutual Information (MI) plays an important role in representation learning. However, MI is unfortunately intractable in continuous and high-dimensional settings. Recent advances establish tractable and scalable MI estimators to discover useful representation. However, most of the existing methods are not capable of providing an accurate estimation of MI with low-variance when the MI is large. We argue that directly estimating the gradients of MI is more appealing for representation learning than estimating MI in itself. To this end, we propose the Mutual Information Gradient Estimator (MIGE) for representation learning based on the score estimation of implicit distributions. MIGE exhibits a tight and smooth gradient estimation of MI in the high-dimensional and large-MI settings. We expand the applications of MIGE in both unsupervised learning of deep representations based on InfoMax and the Information Bottleneck method. Experimental results have indicated significant performance improvement in learning useful representation.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
