Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMaximum likelihood estimation for disk image parameters
122
0
0.0
(
0
)
Authors
Matwey V. Kornilov
Ask ChatGPT about the research
No Arabic abstract
We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise the following advantages of our likelihood model. It has closed-form formulae for parameter estimating, requiring less computational resources than iterative algorithms therefore. The likelihood model naturally distinguishes the outer and inner annulus edges. The proposed technique was evaluated on both synthetic and real data.
rate research
Read More
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i in [0, 1]$ drawn from some unknown distribution $P^star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i sim text{Binomial}(t, p_i)$ per individual, our objective is to accurately estimate $P^star$. This problem arises in numerous domains, including the social sciences, psychology, health-care, and biology, where the size of the population under study is usually large while the number of observations per individual is often limited. Our main result shows that, in the regime where $t ll N$, the maximum likelihood estimator (MLE) is both statistically minimax optimal and efficiently computable. Precisely, for sufficiently large $N$, the MLE achieves the information theoretic optimal error bound of $mathcal{O}(frac{1}{t})$ for $t < clog{N}$, with regards to the earth movers distance (between the estimated and true distributions). More generally, in an exponentially large interval of $t$ beyond $c log{N}$, the MLE achieves the minimax error bound of $mathcal{O}(frac{1}{sqrt{tlog N}})$. In contrast, regardless of how large $N$ is, the naive plug-in estimator for this problem only achieves the sub-optimal error of $Theta(frac{1}{sqrt{t}})$.
LISA is the upcoming space-based Gravitational Wave telescope. LISA Pathfinder, to be launched in the coming years, will prove and verify the detection principle of the fundamental Doppler link of LISA on a flight hardware identical in design to that of LISA. LISA Pathfinder will collect a picture of all noise disturbances possibly affecting LISA, achieving the unprecedented pureness of geodesic motion necessary for the detection of gravitational waves. The first steps of both missions will crucially depend on a very precise calibration of the key system parameters. Moreover, robust parameters estimation is of fundamental importance in the correct assessment of the residual force noise, an essential part of the data processing for LISA. In this paper we present a maximum likelihood parameter estimation technique in time domain being devised for this calibration and show its proficiency on simulated data and validation through Monte Carlo realizations of independent noise runs. We discuss its robustness to non-standard scenarios possibly arising during the real-life mission, as well as its independence to the initial guess and non-gaussianities. Furthermore, we apply the same technique to data produced in mission-like fashion during operational exercises with a realistic simulator provided by ESA.
The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek model, statistical inference for this process is of great interest. Based on continuous time observations, this paper considers the problem of estimating the drift parameters in the mixed fractional Vasicek model. We will propose the maximum likelihood estimators of the drift parameters in the mixed fractional Vasicek model with the Radon-Nikodym derivative for a mixed fractional Brownian motion. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators have been established for all $Hin(0,1)$, $H eq 1/2$.
The Reward-Biased Maximum Likelihood Estimate (RBMLE) for adaptive control of Markov chains was proposed to overcome the central obstacle of what is variously called the fundamental closed-identifiability problem of adaptive control, the dual control problem, or, contemporaneously, the exploration vs. exploitation problem. It exploited the key observation that since the maximum likelihood parameter estimator can asymptotically identify the closed-transition probabilities under a certainty equivalent approach, the limiting parameter estimates must necessarily have an optimal reward that is less than the optimal reward attainable for the true but unknown system. Hence it proposed a counteracting reverse bias in favor of parameters with larger optimal rewards, providing a solution to the fundamental problem alluded to above. It thereby proposed an optimistic approach of favoring parameters with larger optimal rewards, now known as optimism in the face of uncertainty. The RBMLE approach has been proved to be long-term average reward optimal in a variety of contexts. However, modern attention is focused on the much finer notion of regret, or finite-time performance. Recent analysis of RBMLE for multi-armed stochastic bandits and linear contextual bandits has shown that it not only has state-of-the-art regret, but it also exhibits empirical performance comparable to or better than the best current contenders, and leads to strikingly simple index policies. Motivated by this, we examine the finite-time performance of RBMLE for reinforcement learning tasks that involve the general problem of optimal control of unknown Markov Decision Processes. We show that it has a regret of $mathcal{O}( log T)$ over a time horizon of $T$ steps, similar to state-of-the-art algorithms. Simulation studies show that RBMLE outperforms other algorithms such as UCRL2 and Thompson Sampling.
Although deep learning models have driven state-of-the-art performance on a wide array of tasks, they are prone to learning spurious correlations that should not be learned as predictive clues. To mitigate this problem, we propose a causality-based training framework to reduce the spurious correlations caused by observable confounders. We give theoretical analysis on the underlying general Structural Causal Model (SCM) and propose to perform Maximum Likelihood Estimation (MLE) on the interventional distribution instead of the observational distribution, namely Counterfactual Maximum Likelihood Estimation (CMLE). As the interventional distribution, in general, is hidden from the observational data, we then derive two different upper bounds of the expected negative log-likelihood and propose two general algorithms, Implicit CMLE and Explicit CMLE, for causal predictions of deep learning models using observational data. We conduct experiments on two real-world tasks: Natural Language Inference (NLI) and Image Captioning. The results show that CMLE methods outperform the regular MLE method in terms of out-of-domain generalization performance and reducing spurious correlations, while maintaining comparable performance on the regular evaluations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
