This thesis addresses text-independent speaker verification from a machine learning point of view. We use the machine learning framework to better define the problem and to develop new unbiased performance measures and statistical tests to compare objectively new approaches. We propose a new interpretation of the state-of-the-art Gaussian Mixture Model based system and show that they are discriminant and equivalent to a mixture of linear classifiers. A general framework for score normalization is also given for both probability and non-probability based models. With this new framework we better show the hypotheses made for the well known Z- and T- score normalization techniques. Several uses of discriminant models are then proposed. In particular, we develop a new sequence kernel for Support Vector Machines that generalizes an other sequence kernel found in the literature. If the latter is limited to a polynomial form the former allows the use of infinite space kernels such as Radial Basis Functions. A variant of this kernel that finds the best match for each frame of the sequence to be compared, actually outperforms the state-of-the-art systems. As our new sequence kernel is computationally costly for long sequences, a clustering technique is proposed for reducing the complexity. We also address in this thesis some problems specific to speaker verification such as the fact that the classes are highly unbalanced. And the use of a specific intra- and inter-class distance distribution is proposed by modifying the kernel in order to assume a Gaussian noise distribution over negative examples. Even if this approach misses some theoretical justification, it gives very good empirical results and opens a new research direction.