This presentation is a case study taken from the travel and holiday industry. Paxport/Multicom, based in UK and Sweden, have recently adopted a recommendation system for holiday accommodation bookings. Machine learning techniques such as Collaborative Filtering have been applied using Python (3.5.1), with Jupyter (4.0.6) as the main framework. Data scale and sparsity present significant challenges in the case study, and so the effectiveness of various techniques are described as well as the performance of Python-based libraries such as Python Data Analysis Library (Pandas), and Scikit-learn (built on NumPy, SciPy and matplotlib). The presentation is suitable for all levels of programmers.

Machine learning with Python

Deep learning has triggered the current rise of artificial intelligence and is the workhorse of today’s machine intelligence. Numerous success stories have rapidly spread all over science, industry and society, but its limitations have only recently come into focus. In this Perspective we seek to distil how many of deep learning’s failures can be seen as different symptoms of the same underlying problem: shortcut learning. Shortcuts are decision rules that perform well on standard benchmarks but fail to transfer to more challenging testing conditions, such as real-world scenarios. Related issues are known in comparative psychology, education and linguistics, suggesting that shortcut learning may be a common characteristic of learning systems, biological and artificial alike. Based on these observations, we develop a set of recommendations for model interpretation and benchmarking, highlighting recent advances in machine learning to improve robustness and transferability from the lab to real-world applications. Deep learning has resulted in impressive achievements, but under what circumstances does it fail, and why? The authors propose that its failures are a consequence of shortcut learning, a common characteristic across biological and artificial systems in which strategies that appear to have solved a problem fail unexpectedly under different circumstances.

Shortcut learning in deep neural networks

Deep learning has triggered the current rise of artificial intelligence and is the workhorse of today's machine intelligence. Numerous success stories have rapidly spread all over science, industry and society, but its limitations have only recently come into focus. In this perspective we seek to distil how many of deep learning's problem can be seen as different symptoms of the same underlying problem: shortcut learning. Shortcuts are decision rules that perform well on standard benchmarks but fail to transfer to more challenging testing conditions, such as real-world scenarios. Related issues are known in Comparative Psychology, Education and Linguistics, suggesting that shortcut learning may be a common characteristic of learning systems, biological and artificial alike. Based on these observations, we develop a set of recommendations for model interpretation and benchmarking, highlighting recent advances in machine learning to improve robustness and transferability from the lab to real-world applications.

Shortcut Learning in Deep Neural Networks

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

An Empirical Study of Example Forgetting during Deep Neural Network Learning

Several works have proposed Simplicity Bias (SB)---the tendency of standard training procedures such as Stochastic Gradient Descent (SGD) to find simple models---to justify why neural networks generalize well [Arpit et al. 2017, Nakkiran et al. 2019, Soudry et al. 2018]. However, the precise notion of simplicity remains vague. Furthermore, previous settings that use SB to theoretically justify why neural networks generalize well do not simultaneously capture the non-robustness of neural networks---a widely observed phenomenon in practice [Goodfellow et al. 2014, Jo and Bengio 2017]. We attempt to reconcile SB and the superior standard generalization of neural networks with the non-robustness observed in practice by designing datasets that (a) incorporate a precise notion of simplicity, (b) comprise multiple predictive features with varying levels of simplicity, and (c) capture the non-robustness of neural networks trained on real data. Through theory and empirics on these datasets, we make four observations: (i) SB of SGD and variants can be extreme: neural networks can exclusively rely on the simplest feature and remain invariant to all predictive complex features. (ii) The extreme aspect of SB could explain why seemingly benign distribution shifts and small adversarial perturbations significantly degrade model performance. (iii) Contrary to conventional wisdom, SB can also hurt generalization on the same data distribution, as SB persists even when the simplest feature has less predictive power than the more complex features. (iv) Common approaches to improve generalization and robustness---ensembles and adversarial training---can fail in mitigating SB and its pitfalls. Given the role of SB in training neural networks, we hope that the proposed datasets and methods serve as an effective testbed to evaluate novel algorithmic approaches aimed at avoiding the pitfalls of SB.

The Pitfalls of Simplicity Bias in Neural Networks

Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime where classical learning theory would instead predict that they would severely overfit. While many proposals for some kind of implicit regularization have been made to rationalise this success, there is no consensus for the fundamental reason why DNNs do not strongly overfit. In this paper, we provide a new explanation. By applying a very general probability-complexity bound recently derived from algorithmic information theory (AIT), we argue that the parameter-function map of many DNNs should be exponentially biased towards simple functions. We then provide clear evidence for this strong simplicity bias in a model DNN for Boolean functions, as well as in much larger fully connected and convolutional networks applied to CIFAR10 and MNIST. As the target functions in many real problems are expected to be highly structured, this intrinsic simplicity bias helps explain why deep networks generalize well on real world problems. This picture also facilitates a novel PAC-Bayes approach where the prior is taken over the DNN input-output function space, rather than the more conventional prior over parameter space. If we assume that the training algorithm samples parameters close to uniformly within the zero-error region then the PAC-Bayes theorem can be used to guarantee good expected generalization for target functions producing high-likelihood training sets. By exploiting recently discovered connections between DNNs and Gaussian processes to estimate the marginal likelihood, we produce relatively tight generalization PAC-Bayes error bounds which correlate well with the true error on realistic datasets such as MNIST and CIFAR10 and for architectures including convolutional and fully connected networks.

Deep learning generalizes because the parameter-function map is biased towards simple functions.

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Deep learning generalizes because the parameter-function map is biased towards simple functions

Many systems in nature can be described using discrete input-output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity [Formula: see text] of that output. These input-output maps are biased towards simplicity. We derive an upper bound P(x) ≲ [Formula: see text], which is tight for most inputs. The constants a and b, as well as many properties of  P(x), can be predicted with minimal knowledge of the map. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model.

/pdf/input-output-maps-are-strongly-biased-towards-simple-outputs-4bx5qt93o6.pdf

Input-output maps are strongly biased towards simple outputs.

Engineers routinely design systems to be modular and symmetric in order to increase robustness to perturbations and to facilitate alterations at a later date. Biological structures also frequently exhibit modularity and symmetry, but the origin of such trends is much less well understood. It can be tempting to assume -- by analogy to engineering design -- that symmetry and modularity arise from natural selection. But evolution, unlike engineers, cannot plan ahead, and so these traits must also afford some immediate selective advantage which is hard to reconcile with the breadth of systems where symmetry is observed. Here we introduce an alternative non-adaptive hypothesis based on an algorithmic picture of evolution. It suggests that symmetric structures preferentially arise not just due to natural selection, but also because they require less specific information to encode, and are therefore much more likely to appear as phenotypic variation through random mutations. Arguments from algorithmic information theory can formalise this intuition, leading to the prediction that many genotype-phenotype maps are exponentially biased towards phenotypes with low descriptional complexity. A preference for symmetry is a special case of this bias towards compressible descriptions. We test these predictions with extensive biological data, showing that that protein complexes, RNA secondary structures, and a model gene-regulatory network all exhibit the expected exponential bias towards simpler (and more symmetric) phenotypes. Lower descriptional complexity also correlates with higher mutational robustness, which may aid the evolution of complex modular assemblies of multiple components.

/pdf/symmetry-and-simplicity-spontaneously-emerge-from-the-3tcax9nfir.pdf

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution

In 2020, the term ‘infodemic’ rose from relative obscurity to becoming a popular catch-all metaphor, representing the perils of fast, wide-spreading (false) information about the coronavirus pandem...

Chico Q. Camargo

Papers

Deep learning generalizes because the parameter-function map is biased towards simple functions.

Deep learning generalizes because the parameter-function map is biased towards simple functions

Input-output maps are strongly biased towards simple outputs.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution

Autopsy of a metaphor: The origins, use and blind spots of the ‘infodemic’