Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

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Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer's principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg-Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria.T he relationship between information and thermodynamics remains an active area of research despite decades of study (1-4). An important implication of the recent experimental confirmation of Landauer's principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2, 3). The generality of Landauer's argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorumsensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms.A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (5-8). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (9-11), suggesting that these constraints may also influence the design of cellular computing networks.The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (12)(13)(14). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (12). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate k off 4 and unbinds particles at a uniform rate k off 4 (see Fig. 1). They argued that cells could estimate the ambient che...

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