Function-guided protein design by deep manifold sampling

Protein design is challenging because it requires searching through a vast combinatorial space that is only sparsely functional. Self-supervised learning approaches offer the potential to navigate through this space more effectively and thereby accelerate protein engineering. We introduce a sequence denoising autoencoder (DAE) that learns the manifold of protein sequences from a large amount of potentially unlabelled proteins. This DAE is combined with a function predictor that guides sampling towards sequences with higher levels of desired functions. We train the sequence DAE on more than 20M unlabeled protein sequences spanning many evolutionarily diverse protein families and train the function predictor on approximately 0.5M sequences with known function labels. At test time, we sample from the model by iteratively denoising a sequence while exploiting the gradients from the function predictor. We present a few preliminary case studies of protein design that demonstrate the effectiveness of this proposed approach, which we refer to as "deep manifold sampling", including metal binding site addition, function-preserving diversification, and global fold change.

Cross-Validation Model Averaging for Generalized Functional Linear Model

Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model averaging method for generalized functional linear model where the scalar response variable is related to a random function predictor by a link function. We establish asymptotic theoretical result on the optimality of the weights selected by our method when the true model is not in the candidate model set. Our simulations show that the proposed method often performs better than the commonly used model selection and averaging methods. We also apply the proposed method to Beijing second-hand house price data.

OPTIMIZATION OF UNIMODAL FUNCTIONS USING PARABOLIC PREDICTOR search

A combined parabolic predictor search is proposed for the conditional minimization of the unimodal function using the predictive-based selective application of phases of extremum search by golden section search and parabolic search. The formula for calculating the value of parabolic predictor function is given, with its help it is possible to work out the forecast and tactics of extremum search of the minimized function. Predictor includes forecasting extremeness, monotony and constancy of function on a segment of uncertainty. Identification forecast for a direct function is described, using which allows to find a solution in three calculations. The assertion is made that if three successive computations of a function give points with similar ordinates, then abscissa of each point can be a solution of the problem. The procedure of identifying non-direct monotonic functions is described. It is shown that the reliability of monotonicity forecast can be determined by five calculations of the function. There has been described the procedure of using phases of parabolic method, which can be performed at favorable prediction of detecting the internal extremum of function. It has been stated that carrying out these phases, even with favorable forecast, can be considered inexpedient for cases when it is recognized that the problem is weakly sensitive or insensitive to the parabolic forecast. Block diagrams of algorithms implementing the method are given. It is shown that, compared to golden section search, the predictor has 3-5 times faster response for smooth functions and is comparable by this criterion to Brent method. The predictor achieves the greatest speed when minimizing monotonic functions. The method works somewhat slower than golden section search, however, it is much faster than Brent method when searching for the minimum of piecewise, flat, planar and other functions of a similar nature for which approximation of parabola does not give the expected effect. In comparison with Brent method, parabolic predictor has 1.5-4 times more speed in solving problems of such type.