**TherML**

In this work we offer a framework for reasoning about a wide class of existing objectives in machine learning. We develop a formal correspondence between this work and thermodynamics and discuss its implications. … **TensorFlow Probability**

TensorFlow Probability is a library for probabilistic reasoning and statistical analysis in TensorFlow. As part of the TensorFlow ecosystem, TensorFlow Probability provides integration of probabilistic methods with deep networks, gradient-based inference via automatic differentiation, and scalability to large datasets and models via hardware acceleration (e.g., GPUs) and distributed computation. … **List-Decodable Linear Regression**

We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $_{i \leq n}$ of $n$ linear equations where $\alpha n$ of the equations satisfy $y_i = \langle x_i,\ell^*\rangle +\zeta$ for some small noise $\zeta$ and $(1-\alpha)n$ of the equations are \emph{arbitrarily} chosen. It outputs a list $L$ of size $O(1/\alpha)$ – a fixed constant – that contains an $\ell$ that is close to $\ell^*$. Our algorithm succeeds whenever the inliers are chosen from a \emph{certifiably} anti-concentrated distribution $D$. As a special case, this yields a $(d/\alpha)^{O(1/\alpha^8)}$ time algorithm to find a $O(1/\alpha)$ size list when the inlier distribution is a standard Gaussian. The anti-concentration assumption on the inliers is information-theoretically necessary. Our algorithm works for more general distributions under the additional assumption that $\ell^*$ is Boolean valued. To solve the problem we introduce a new framework for list-decodable learning that strengthens the sum-of-squares `identifiability to algorithms’ paradigm. In an independent work, Raghavendra and Yau [RY19] have obtained a similar result for list-decodable regression also using the sum-of-squares method. … **Individual Survival Distribution (ISD)**

An accurate model of a patient’s individual survival distribution can help determine the appropriate treatment for terminal patients. Unfortunately, risk scores (e.g., from Cox Proportional Hazard models) do not provide survival probabilities, single-time probability models (e.g., the Gail model, predicting 5 year probability) only provide for a single time point, and standard Kaplan-Meier survival curves provide only population averages for a large class of patients meaning they are not specific to individual patients. This motivates an alternative class of tools that can learn a model which provides an individual survival distribution which gives survival probabilities across all times – such as extensions to the Cox model, Accelerated Failure Time, an extension to Random Survival Forests, and Multi-Task Logistic Regression. This paper first motivates such ‘individual survival distribution’ (ISD) models, and explains how they differ from standard models. It then discusses ways to evaluate such models – namely Concordance, 1-Calibration, Brier score, and various versions of L1-loss – and then motivates and defines a novel approach ‘D-Calibration’, which determines whether a model’s probability estimates are meaningful. We also discuss how these measures differ, and use them to evaluate several ISD prediction tools, over a range of survival datasets. …

# If you did not already know

**04**
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May 2021

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