The Lottery Ticket Hypothesis from Frankle & Carbin (2019) conjectures that, for typically-sized neural networks, it is possible to find small sub-networks which train faster and yield superior performance than their original counterparts. The proposed algorithm to search for "winning tickets", Iterative Magnitude Pruning, consistently finds sub-networks with $90-95\%$ less parameters which train faster and better than the overparameterized models they were extracted from, creating potential applications to problems such as transfer learning. In this paper, we propose Continuous Sparsification, a new algorithm to search for winning tickets which continuously removes parameters from a network during training, and learns the sub-network's structure with gradient-based methods instead of relying on pruning strategies. We show empirically that our method is capable of finding tickets that outperforms the ones learned by Iterative Magnitude Pruning, and at the same time providing faster search, when measured in number of training epochs or wall-clock time.

Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general method for differentiating rank-based metrics with mini-batch gradient descent. In addition, we address optimization instability and sparsity of the supervision signal that both arise from using rank-based metrics as optimization targets. Resulting losses based on recall and Average Precision are applied to image retrieval and object detection tasks. We obtain performance that is competitive with state-of-the-art on standard image retrieval datasets and consistently improve performance of near state-of-the-art object detectors.

Question classification (QC) is the primary step of the Question Answering (QA) system. Question Classification (QC) system classifies the questions in particular classes so that Question Answering (QA) System can provide correct answers for the questions. Our system categorizes the factoid type questions asked in natural language after extracting features of the questions. We present a two stage QC system for Bengali. It utilizes one dimensional convolutional neural network for classifying questions into coarse classes in the first stage. Word2vec representation of existing words of the question corpus have been constructed and used for assisting 1D CNN. A smart data balancing technique has been employed for giving data hungry convolutional neural network the advantage of a greater number of effective samples to learn from. For each coarse class, a separate Stochastic Gradient Descent (SGD) based classifier has been used in order to differentiate among the finer classes within that coarse class. TF-IDF representation of each word has been used as feature for the SGD classifiers implemented as part of second stage classification. Experiments show the effectiveness of our proposed method for Bengali question classification.

Data privacy and security becomes a major concern in building machine learning models from different data providers. Federated learning shows promise by leaving data at providers locally and exchanging encrypted information. This paper studies the vertical federated learning structure for logistic regression where the data sets at two parties have the same sample IDs but own disjoint subsets of features. Existing frameworks adopt the first-order stochastic gradient descent algorithm, which requires large number of communication rounds. To address the communication challenge, we propose a quasi-Newton method based vertical federated learning framework for logistic regression under the additively homomorphic encryption scheme.

Stephanie L. Hyland Microsoft Research Shruti Tople Microsoft Research Abstract --Protecting the privacy of training data is important for the safe deployment of machine learning models. Private learning algorithms have been proposed that ensure strong differential-privacy (DP) guarantees. However, the additional noise required for such protection comes at the cost of reduced model utility. Meanwhile, the stochastic gradient descent (SGD) method -- the most common optimization algorithm for neural networks -- contains intrinsic randomness which has not been leveraged for privacy. Arguing that SGD guarantees intrinsic privacy, we investigate the extent to which this privacy can be quantified and used to improve the utility of privately learned models. In effect, we ask the question; "If SGD were a differentially-private mechanism, how good would it be?" In this work, we take the first step towards analysing the intrinsic privacy properties of SGD. Our primary contribution is a large-scale empirical analysis of SGD on both convex and non-convex objectives. T o this end, we evaluate the inherent variability due to the stochasticity in SGD on 3 different datasets and calculate the null values due to the intrinsic noise. First, we show that the variability in model parameters due to the random sampling almost always exceeds that due to changes in the data. We observe that SGD provides intrinsic null values of 7. 8, 6 .9 Next, we propose a method to augment the intrinsic noise of SGD with additional noise to achieve the desired null. Our augmented SGD outputs model that outperform existing approaches with the same privacy guarantee, thus closing the gap to noiseless utility between 0 . Finally, we show that the existing theoretical bound on the sensitivity of SGD is not tight. By estimating the tightest bound empirically, we achieve near-noiseless performance at null 1, closing the utility gap to the noiseless model between 3 . Our experiments provide concrete evidence that changing the seed in SGD is likely to have a far greater impact on the resulting model than including or excluding any given training example. By properly accounting for this intrinsic randomness, higher utility can be achieved without sacrificing further privacy. With these results, we hope to inspire the research community to further explore and characterise the randomness in SGD, its impact on privacy, and the parallels with generalisation in machine learning. I NTRODUCTION Respecting the privacy of users contributing their data to train machine learning models is important.

The field of machine learning underwent massive changes in the 2010's. At the beginning, the field saw diverse approaches applied to a variety of topics and data structures. Then Alexnet blew away the competition for the Imagenet challenge with his CNN, and the field was forever changed. However, there was a warming up phase. Caffe's first release was in 2013.

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance, we prove that (in the worst case) any algorithm requires at least $\epsilon^{-4}$ queries to find an $\epsilon$ stationary point. The lower bound is tight, and establishes that stochastic gradient descent is minimax optimal in this model. In a more restrictive model where the noisy gradient estimates satisfy a mean-squared smoothness property, we prove a lower bound of $\epsilon^{-3}$ queries, establishing the optimality of recently proposed variance reduction techniques.

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the energy-time uncertainty relation from quantum mechanics, we propose a Quantum-Inspired Hamiltonian Monte Carlo algorithm (QHMC). This algorithm allows a particle to have a random mass with a probability distribution rather than a fixed mass. We prove the convergence property of QHMC in the spatial domain and in the time sequence. We further show why such a random mass can improve the performance when we sample a broad class of distributions. In order to handle the big training data sets in large-scale machine learning, we develop a stochastic gradient version of QHMC using Nos\'e-Hoover thermostat called QSGNHT, and we also provide theoretical justifications about its steady-state distributions. Finally in the experiments, we demonstrate the effectiveness of QHMC and QSGNHT on synthetic examples, bridge regression, image denoising and neural network pruning. The proposed QHMC and QSGNHT can indeed achieve much more stable and accurate sampling results on the test cases.

Data privacy and security becomes a major concern in building machine learning models from different data providers. Federated learning shows promise by leaving data at providers locally and exchanging encrypted information. This paper studies the vertical federated learning structure for logistic regression where the data sets at two parties have the same sample IDs but own disjoint subsets of features. Existing frameworks adopt the first-order stochastic gradient descent algorithm, which requires large number of communication rounds. To address the communication challenge, we propose a quasi-Newton method based vertical federated learning framework for logistic regression under the additively homomorphic encryption scheme. Our approach can considerably reduce the number of communication rounds with a little additional communication cost per round. Numerical results demonstrate the advantages of our approach over the first-order method.

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel Hilbert space norm. This construction leads to interacting particle systems, the mean-field limit of which is a gradient flow on the space of probability distributions equipped with a certain geometrical structure. We leverage this viewpoint to shed some light on the convergence properties of the algorithm, in particular addressing the problem of choosing a suitable positive definite kernel function. Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performs gains of these in various numerical experiments.