Numerical resolution of optimal stopping problems has been an active area of research for more than two decades. Originally investigated in the context of American Option pricing, it has since metamorphosed into a field unto itself, with numerous wide-ranging applications and dozens of proposed approaches. A major strand, which is increasingly dominating the subject, is simulation-based methods rooted in the Monte Carlo paradigm. Developed in the late 1990s in [23] and [31] this framework remains without an agreed-upon name; we shall refer to it as Regression Monte Carlo (RMC). The main feature of RMC is its marriage of a probabilistic approach, namely simulation of the underlying stochastic state dynamics, and statistical tools for approximating the quantities of interest: the value and/or continuation functions, and the stopping region.

It is common to aggregate information and evaluate items by collecting ratings on these items from people. In this work, we focus on the bias introduced by people's observable outcome or experience from the entity under evaluation, and we call it the "outcome-induced bias". Let describe this notion of bias with the help of two common applications - teaching evaluation and peer review. Many universities use student ratings for teaching evaluation. However, numerous studies have shown that student ratings are affected by the grading policy of the instructor [16, 26, 5]. For instance, as noted in [26, Chapter 4]: "...the effects of grades on teacher-course evaluations are both substantively and statistically important, and suggest that instructors can often double their odds of receiving high evaluations from students simply by awarding A's rather than B's or C's." As a consequence, the association between student ratings and teaching effectiveness can become negative [5], and student ratings serve as a poor predictor on the follow-on course achievement of the students [8, 6]: "...teachers who are associated with better subsequent performance receive worst evaluations from their students."

Communication constraints are one of the major challenges preventing the wide-spread adoption of Federated Learning systems. Recently, Federated Distillation (FD), a new algorithmic paradigm for Federated Learning with fundamentally different communication properties, emerged. FD methods leverage ensemble distillation techniques and exchange model outputs, presented as soft labels on an unlabeled public data set, between the central server and the participating clients. While for conventional Federated Learning algorithms, like Federated Averaging (FA), communication scales with the size of the jointly trained model, in FD communication scales with the distillation data set size, resulting in advantageous communication properties, especially when large models are trained. In this work, we investigate FD from the perspective of communication efficiency by analyzing the effects of active distillation-data curation, soft-label quantization and delta-coding techniques. Based on the insights gathered from this analysis, we present Compressed Federated Distillation (CFD), an efficient Federated Distillation method. Extensive experiments on Federated image classification and language modeling problems demonstrate that our method can reduce the amount of communication necessary to achieve fixed performance targets by more than two orders of magnitude, when compared to FD and by more than four orders of magnitude when compared with FA.

High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far, inconsistencies can occur among the tasks in terms of data geometry and others. This can lead to confusing or misleading data interpretation. In this paper, we propose a novel neural network-based method, called Consistent Representation Learning (CRL), to accomplish the three associated tasks end-to-end and improve the consistencies. The CRL network consists of two nonlinear dimensionality reduction (NLDR) transformations: (1) one from the input data space to the latent feature space for clustering, and (2) the other from the clustering space to the final 2D or 3D space for visualization. Importantly, the two NLDR transformations are performed to best satisfy local geometry preserving (LGP) constraints across the spaces or network layers, to improve data consistencies along with the processing flow. Also, we propose a novel metric, clustering-visualization inconsistency (CVI), for evaluating the inconsistencies. Extensive comparative results show that the proposed CRL neural network method outperforms the popular t-SNE and UMAP-based and other contemporary clustering and visualization algorithms in terms of evaluation metrics and visualization.

Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses normalizing flows to provide a rich family of flexible branch length distributions that generalize across different tree topologies. We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems. Further investigation also reveals that the structured parameterization in those permutation equivariant transformations can provide additional amortization benefit.

Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, such as context-free grammars, have been used to limit the search spaces in equation discovery by providing hard constraints that specify which equations to consider and which not. In this paper, we propose the use of probabilistic context-free grammars in the context of equation discovery. Such grammars encode soft constraints on the space of equations, specifying a prior probability distribution on the space of possible equations. We show that probabilistic grammars can be used to elegantly and flexibly formulate the parsimony principle, that favors simpler equations, through probabilities attached to the rules in the grammars. We demonstrate that the use of probabilistic, rather than deterministic grammars, in the context of a Monte-Carlo algorithm for grammar-based equation discovery, leads to more efficient equation discovery. Finally, by specifying prior probability distributions over equation spaces, the foundations are laid for Bayesian approaches to equation discovery.

We use gradient sparsification to reduce the adverse effect of differential privacy noise on performance of private machine learning models. To this aim, we employ compressed sensing and additive Laplace noise to evaluate differentially-private gradients. Noisy privacy-preserving gradients are used to perform stochastic gradient descent for training machine learning models. Sparsification, achieved by setting the smallest gradient entries to zero, can reduce the convergence speed of the training algorithm. However, by sparsification and compressed sensing, the dimension of communicated gradient and the magnitude of additive noise can be reduced. The interplay between these effects determines whether gradient sparsification improves the performance of differentially-private machine learning models. We investigate this analytically in the paper. We prove that, for small privacy budgets, compression can improve performance of privacy-preserving machine learning models. However, for large privacy budgets, compression does not necessarily improve the performance. Intuitively, this is because the effect of privacy-preserving noise is minimal in large privacy budget regime and thus improvements from gradient sparsification cannot compensate for its slower convergence.

This three part write up [Part II Part III] is my attempt at a down-to-earth explanation (and Python code) of the Holt-Winters method for those of us who while hypothetically might be quite good at math, still try to avoid it at every opportunity. I had to dive into this subject while tinkering on tgres (which features a Golang implementation). And having found it somewhat complex (and yet so brilliantly simple), figured that it'd be good to share this knowledge, and in the process, to hopefully solidify it in my head as well. Triple Exponential Smoothing, also known as the Holt-Winters method, is one of the many methods or algorithms that can be used to forecast data points in a series, provided that the series is "seasonal", i.e. repetitive over some period. In 1957 an MIT and University of Chicago graduate, professor Charles C Holt (1921-2010) was working at CMU (then known as CIT) on forecasting trends in production, inventories and labor force.

If you have ever done a Kaggle competition, these would be commonly referred to as evaluation metrics. Typically, the lower the loss, the better the performance of your model. So if,for example, you were predicting house prices and using Mean Squared Error, and your cost was $25000, that means that your model is performing poorly as it is making a prediction error of $25000. Going back to our analogy, if you imagine that instead of a mountain there is a U-shaped curve, and instead of a person there is the cost function with maybe an initial cost value of 25,500. The aim of Gradient Descent would be to minimise this cost to either 0(global minimum), or something much smaller(local minimum).

Online Courses Udemy - All-in-One:Machine Learning,DL,NLP,AWS Deply [Hindi][Python], Complete hands-on Machine Learning Course with Data Science, NLP, Deep Learning and Artificial Intelligence Created by Rishi Bansal English Students also bought Java from Zero to First Job: Part 1 - Java Basics and OOP C Programming for Beginners - Master the C Fundamentals Full-Stack Web Development For Beginners The Complete Java Programmer: From Scratch to Advanced Python and Django Full-Stack Web Development for beginners Learn To Create AI Assistant (JARVIS) With Python Preview this course GET COUPON CODE Description This course is designed to cover maximum Concept of Machine Learning. Anyone can opt for this course. No prior understanding of Machine Learning is required. As a Bonus Introduction Natural Language Processing and Deep Learning is included. Below Topics are covered Chapter - Introduction to Machine Learning - Machine Learning?