The compressive learning framework reduces the computational cost of training on large-scale datasets. In a sketching phase, the data is first compressed to a lightweight sketch vector, obtained by mapping the data samples through a well-chosen feature map, and averaging those contributions. In a learning phase, the desired model parameters are then extracted from this sketch by solving an optimization problem, which also involves a feature map. When the feature map is identical during the sketching and learning phases, formal statistical guarantees (excess risk bounds) have been proven. However, the desirable properties of the feature map are different during sketching and learning (e.g. quantized outputs, and differentiability, respectively). We thus study the relaxation where this map is allowed to be different for each phase. First, we prove that the existing guarantees carry over to this asymmetric scheme, up to a controlled error term, provided some Limited Projected Distortion (LPD) property holds. We then instantiate this framework to the setting of quantized sketches, by proving that the LPD indeed holds for binary sketch contributions. Finally, we further validate the approach with numerical simulations, including a large-scale application in audio event classification.

翻译：压缩学习框架降低了大规模数据集培训的计算成本。 在素描阶段,数据首先压缩为轻量素描矢量,通过精心选择的地貌图绘制数据样本,并平均贡献。在学习阶段,理想的模型参数随后通过解决优化问题从素描中提取,这也涉及地貌图。当特征图在素描和学习阶段完全相同时,正式的统计保证(过大的风险界限)已经得到证明。然而,在素描和学习期间,特征图的可取性是不同的(例如,量化产出和可变性)。因此,我们研究了允许该地图在每一阶段有差异的放松程度。首先,我们证明现有的保证将延续到这一不对称计划,直到一个有控制的错误期,提供了一些有限的预测扭曲性(LPD)属性的保存。然后,我们将这一框架转而用于确定量化的草图,证明LPD确实用于二进制素材。最后,我们用数字模拟活动进一步验证了方法,包括音频级的大规模应用。