The paper tackles a timely area of research, namely new approaches for time-to-event data modeling which is common in health data analysis. There is a large body of statistics literature on this topic and some recent ML approaches, such as DeepSurvival (Blei lab) and DeepHit (van der Shaar lab). The work proposes a multi-task model to consider competing risks, similar to DeepHit. The authors do compare with other methods, but I think these comparisons fail in two aspects: a) no comparison with a version of their method that considers each risk independently -- this comparison would be important to include in order to understand whether it is the flexibility from boosting trees or from the simultaneous modeling of multiple risks that leads to the improved performance. Apart from the limitations in the results part, I thought that the presentation of the methodology as a boosting method is not very clear.

Summary The paper investigates the kernel k-means problem, proposing a new approximation of the method based on Nystrom embeddings. In particular, both the statistical accuracy and computational efficiency of the proposed approximation is studied. The main contribution is the derivation of a theoretical bound limiting the error cost; the proposed method can achieve such theoretical guarantee with a computational cost of (O(\sqrt{n})). In practice, this implies that using \sqrt{n} points (with n being the original sample size) is enough to obtain a good enough approximation. The authors also propose an approach to choose the points while ensuring a balance trade off between preserving a good approximation and a small complexity (dictionary size).

This paper introduces a smooth thresholding technique which enables practically standard gradient descent optimization to be applied to spiking neural networks. Since the spiking threshold is usually set at a certain membrane potential, the function "spike or no spike" is a function of voltage whose distributional derivative is a dirac Delta at the threshold. By replacing this Dirac delta by a finite positive function g(v) with tight support around the threshold, and which integrates to 1, the step function "spike or no spike" is replaced by a function that increases continuously from 0 to 1 across the support of g. In turn, this setup can be placed into standard differential equation models governing spikes, while retaining the possibility of having meaningful gradient signal for parameter optimization. Two experiments are evaluated, an autoencoding task and a delayed-memory-XOR task, which are both shown to be trainable with the proposed setup.

The authors develop a dimensionality reduction method to identify a low-dimensional representation of olfactory responses in Piriform cortex. Each trial is embedded in a low-dimensional space, and for each neuron a different nonlinear mapping is learned to predict firing rate from this low-dimensional embedding. The nonlinear mapping is parameterized by a Gaussian Process with a relatively smooth prior, which aids in interpretability. The authors assume and exploit Kronecker structure in the noise covariance matrix of the learned model, and describe efficient methods for variational inference. I think this method could be very useful in other experimental systems--not just piriform cortex.

This paper proposes a novel Bayesian Optimization approach that is able to do transfer learning across tasks while remaining scalable. Originality: This is very original work. Bayesian Optimization can work with any probabilistic regression algorithm, so the use of Bayesian linear regression to make it more scalable is well-known, as are its limitations (e.g. it doesn't extrapolate well). The main novelty here lies in the extension to multi-task learning, which allows it to benefit from prior evaluations on previous tasks. When such evaluations are available, this can provide a significant advantage.

In this setting, each user (holding one data point) is required to send a differentially private signal to the server without any prior interaction with the server or other users. Then, the server collects the users' signals and uses them to solve the ERM problem. The most relevant previous work is [19] that shows that any protocol that is based on first (or second) order methods (e.g., gradient descent and other variants) must require sample size \Omega(\alpha {-p}) if it were to achieve error \alpha (where p is the dimensionality of the parameter space). This reference also gives upper bounds of the same order for non-interactive ERM under Local Differential Privacy (LDP) for the class of Lipschitz loss functions and the class of Lipschitz, convex loss functions. This paper revisits this problem under some smoothness assumptions on the loss function, and devises new algorithms for this problem based on polynomial approximation techniques.

The main contribution of the paper can be summarized in two results (stated in the inclusion following line 83): - local saddles are stable for GDA (under Assumption 8.1) - stable equilibria of GDA are also stable for OGDA. Quality: The results are interesting, and the paper is well written. There are some typos in the proofs, but I believe these are omissions that can be corrected, rather than major flaws. Significance: I would love to see further discussion of the consequences of this result, and its relevance to the NIPS community, both theoreticians and practitioners. For example, do these results suggest that GDA should be preferred to OGDA (since the latter has a larger equilibrium set)?

POST REBUTTAL: I do think that the edit to the proof suggested by the authors could work, but would lead to some exorbitant constant C4, a subject not addressed by the authors. Still, I have increased my score from "clear reject" to "accept" in the light of the fact that I am now happy with the validity of the proofs.

The paper proposes a stochastic nested variance reduced gradient descent method for non-convex finite-sum optimization. It has been studied that variance reduction in stochastic gradient evaluations improves the complexity of stochastic gradient evaluations. A popular method is stochastic variance reduced gradient (SVRG), which uses a single reference point to evaluate the gradient. Inspired by this, authors introduce variance reduction using multiple reference points with nested scheme. More precisely, each reference point updates in every T steps and the proposed algorithm uses K points and hence one-epoch iterates T K loops.

The paper proposes a generalization of the KMeans Algorithm by introducing non-negative parameters alpha and beta. The motivation is that different instances of clustering problems may cluster well according to different clustering objectives. The optimal parameter configuration of alpha and beta defines an optimal choice, from the proposed family of clustering algorithms. The paper offers several theoretical contributions. It provides guarantees for the number of samples necessary such that the empirically best parameter set yields clustering costs is within epsilon bounds of the optimal parameters. It provides an algorithm for the enumeration of all possible sets of initial centers for any alpha-interval.